How did Dumbledore know that Harry would believe Snape?

Question

Please watch this to know what I'm talking about.

Dumbledore tells Snape that he must tell Harry something when Voldemort is at his most weakest. Although Harry failed many times to curse Snape at the end of HBP, he was still livid and most likely would and had intent to kill him if given the chance. After all, Snape was the one who took the life of one of Harry's most favoured figure: Dumbledore.

“Precisely. If there comes a time when Lord Voldemort stops sending that snake forth to do his bidding, but keeps it safe beside him under magical protection, then, I think, it will be safe to tell Harry.”

- Harry Potter and the Deathly Hallows, Ch. 33: The Prince's Tale

How did Dumbledore ever think that Harry Potter would listen and even believe one of his most hated enemies? I realize that Snape is more powerful than Harry and could, and most likely would bind Harry with a spell to not let him move, however, why would Harry believe him?

Answer 1

Your question is: Why did Dumbledore think Harry would believe Severus?

Authentication is always crucial while relaying critical information; and as prats110892 notes, this, given Snape's cunning and access to the pensieve and Dumbledore's portrait together with Harry (once he found him), was not impossible.

Another motivation for Dumbledore's judgement lies in one of his good guesses/speculations that Harry himself suspected that the bond between him and Voldemort was deepening. We see that Dumbledore - later in the same conversation as in the question - mentions (Emphasis mine):

“Meanwhile, the connection between them grows ever stronger, a parasitic growth: Sometimes I have thought he suspects it himself. If I know him, he will have arranged matters so that when he does set out to meet his death, it will truly mean the end of Voldemort.”

- Harry Potter and the Deathly Hallows, Ch. 33: The Prince's Tale

It may as well be that he trusted Harry to realize that the connection was much more than a mere telepathy. He claims to know Harry, after all. So even though, as E. J.'s answer already mentions (and is quite evident from this chapter), Dumbledore trusted Snape to competently carry out this task as he had done countless others, in the end he rested all his hopes on Harry to make the 'connection' once Snape had, by any means, succeeded in getting the message across; and acknowledge the truth about the bond, given all the effects of the scar that he had experienced and use it to defeat Voldemort.

After all, he arranged Harry's Occlumency lessons with Snape, of all people, and expected Harry (albeit a little too much) to not mind that and realize the underlying importance of mastering the skill to keep Voldemort at bay. I sense a parallel here as well.

(The only canon answer I could find to the question, and a first for me too :D)

Answer 2

Dumbledore was well aware of the animosity between Snape and Harry: at the end of OoP he recognized that his having Snape tutor Harry had backfired, terribly. Snape was too angry at Harry's father (as well as too emotionally repressed in general) to be open with Harry, and Harry too resentful of Snape to revise his opinion of him very much, even after the Pensieve incident. Yet--as other Hogwarts professors regretfully noted after Dumbledore's death--he had always put an enormous amount of trust in Snape. Dumbledore's opinion of Snape's capacities was very high. As a result, he wants Snape to:

1. Kill him
2. Continue working as a double agent
3. Become headmaster of Hogwarts
4. Protect Hogwarts students from the Carrows
5. Help Harry get the Gryffindor sword
6. Inform Harry that Harry has to let Voldemort kill him

Most people would probably be overwhelmed doing one of those things: Dumbledore asks Snape to do all six, despite the challenge posed by Harry's animosity. Dumbledore knew that Snape was a very inventive person and would probably have little trouble getting the sword to Harry. As for informing Harry, most likely Dumbledore expected Snape to use the Pensieve. Dumbledore had given Harry a rather thorough education in how Pensieves function by using one to show Harry his own memories. By having Harry assist with Slughorn's corrupted memory, Dumbledore ensured that Harry knew how to tell the difference between real and falsified memories. Nothing about Snape's death proved his innocence, and an untaught Harry could have concluded that Snape's memories were fakes, a last attempt at revenge. But Harry never wondered whether the memories were accurate. Dumbledore's instruction ensured that much.

Yes, getting Harry to actually look in the Pensieve could have been complicated, since he was far away from Hogwarts hunting the Horcruxes. But--so long as Harry was not worried about getting cursed while putting his head in the Pensieve--he might not have needed an enormous amount of persuasion to observe Snape's memories. Harry was used to looking into Voldemort's mind, and if he thought Snape knew something that he might need, then he would probably have taken the chance.

Answer 3

So this answers the scenario without the coincidence of Snape dying.

There are multiple ways. All Harry needed was proof and that was available through memories or talk to Dumbledore's portrait. All Snape had to do was get Harry a message as to where he could find the memories or get to Dumbledore's portrait.

1. First - confoundus charm on someone Harry trusts. Maybe Ron. He did use it on Mundungus for the idea of seven potters.
2. Second - his Doe patronus. As we know Harry would already trust the Doe patronus because it led him to the sword of Gryffindor and we also know that the Order used patronuses to relay messages. And Snape being a part of the order would know how to do that. Sure the voice of the message will the be the creator of the patronus but when harry hears Snape's voice from a patronus he trusts he will definitely follow that lead till he is satisfied of his curiosity.
3. Finally - Harry was so angry with Snape that Snape could have simply set a trap for him and once the confrontation happens put a full body bind on Harry till he is shown the complete truth. Snape obviously is a much more powerful wizard than Harry and will most certainly overpower him when it comes to a duel.

Answer 4

The whole story was so terrible, fit in everything that Harry knew and it answered such an amount of questions (Why did Dumbledore trusted Snape ? Why was the hand blackened ? Why was Dumbledore so reluctant to tell Harry the truth that he must die ?) that if Harry would listen, there was no reason not to believe it. So the question is only how Snape could deliver the explanation.

Curiosity was an exploitable weakness of Harry (Harry followed the doe patronus to retrieve the Godric's sword), so this would be one option, but I think there is one surefire way for Snape to force Harry to listen:

Legilimency

In all the hours he and Harry learned together, it was evident that Harry was excruciatingly poor at Occlumency and Snape an accomplished Legilimens. In all their former meetings Snape did also the utmost to hide his memories, so if he really wanted to send memories, Harry could do nothing to prevent it.