Why was Trelawney's first prophecy taken so seriously by everyone?

Question

(heavy spoilers ahead - read at own risk)

As we know the events around the first prophecy of Trelawney go like this:

• Dumbledore interviews her
• She makes the prophecy
• They are interrupted by Snape who overhears part of the prophecy
• Snape rushes to Voldemort and reports what he did overhear
• Meanwhile Dumbledore decides to hire Trelawney (although this might be just for her safety) and let children waste their time with a pointless subject
• Voldemort tries to kill Harry but fails

Here is the quote from Harry Potter and The Half Blood Prince chapter 25:

'Please let me finish.' Dumbledore waited until Harry had nodded curtly, then went on. 'Professor Snape made a terrible mistake. He was still in Lord Voldemort's employ on the night he heard the first half of Professor Trelawney's prophecy. Naturally, he hastened to tell his master what he had heard, for it concerned his master most deeply. But he did not know - he had no possible way of knowing - which boy Voldemort would hunt from then onwards, or that the parents he would destroy in his murderous quest were people that Professor Snape knew, that they were your mother and father -'

Why does everyone - Snape, Dumbledore and Voldemort take this prophecy so seriously?

We have multiple examples where Voldemort does not take it easy if someone wastes his time with pointless news - the punishment for that is heavy. So Snape must have been 100% sure that what he overheads is important.

How was Snape sure that the whole thing wasn't a fraud from Trelawney to get the job?

Voldemort also takes everything very seriously and starts hunting down the Potters with the idea to do something that is evil even by his standards - to kill a toddler. Again based on what? On something that one of his servants heard and nothing more?

Dumbledore seems to think that the prophecy is actually not relevant by itself and becomes important BECAUSE Voldemort acted on it:

"Yes — just love," said Dumbledore. "But Harry, never forget that what the prophecy says is only significant because Voldemort made it so. I told you this at the end of last year. Voldemort singled you out as the person who would be most dangerous to him — and in doing so, he made you the person who would be most dangerous to him!"

"But it comes to the same —"

"No, it doesn't!" said Dumbledore, sounding impatient now. Pointing at Harry with his black, withered hand, he said,

"You are setting too much store by the prophecy!"

"But," spluttered Harry, "but you said the prophecy means —“

"If Voldemort had never heard of the prophecy, would it have been fulfilled? Would it have meant anything? Of course not! Do you think every prophecy in the Hall of Prophecy has been fulfilled?"

This is of course Dumbledore's guess but we know that his guesses are usually true :)

So besides being a major plot driver - is there any in-universe explanation about the behaviour of the people who heard the prophecy.

Answer 1

1. Dumbledore takes it seriously because her ancestor was a famous Seer...

   I had gone there to see an applicant for the post of Divination teacher, though it was against my inclination to allow the subject of Divination to continue at all. The applicant, however, was the great-great-granddaughter of a very famous, very gifted Seer and I thought it common politeness to meet her. (OoTP, Ch 37: The Lost Prophecy)

2. ... and because she acts in a special way (different voice) when making a Prophecy, so it's clear she's not being the typical conwoman Divinator

   {{Dumbledore's Pensieve memory}} But when Sybill Trelawney spoke, it was not in her usual ethereal, mystic voice, but in the harsh, hoarse tones Harry had heard her use once before:
   “The one with the power to vanquish the - Dark Lord approaches .... (OoTP, Ch 37)

3. Snape and Voldemort also take it seriously for the same reasons, AND because Dumbledore was actively listening to it as if it was for realz, not shutting her down immediately.

Answer 2

It's quite simple actually. When the prophecy was made, everyone was much younger. The potters and snape were in their twenties, as well as tom riddle who began making horcruxes while he was in school.

Snaps hearing the prophecy would have run to voldy no matter what because it was news of a pending threat no matter how remote.

Tom was forced to respond because the prophecy gave the resistance something to rally against. Something to give them hope, and this hope must be squashed out and he had to prove he was better than anything a silly prophecy could conjure up.

The prophecy happened when it did otherwise it could not have been fulfilled. It's very anthropocentric, it happened because we were there to see it happen.

However, don't forget this isn't trelawney's only prophecy, she had another trance prophecy, and potentially a third with the whole "grim" / Sirius black thing depending on how you chose to place your point of view.