How did Snape sense Quirrell's curse to apply countercurse?

Question

‘But Snape tried to kill me!’

‘No, no, no. I tried to kill you. Your friend Miss Granger accidentally knocked me over as she rushed to set fire to Snape at that Quidditch match. She broke my eye contact with you. Another few seconds and I’d have got you off that broom. I’d have managed it before then if Snape hadn’t been muttering a countercurse, trying to save you.’

_{Philosopher's Stone - page 209 - Bloomsbury - chapter seventeen, The Man With Two Faces - Harry Potter and Professor Quirrell}

Since Snape is a good guy, it's safe to assume that he didn't see Quirrell performing a curse on Harry. Otherwise, he would have reported it to Dumbledore.

Also, since no other wizard there was applying a countercurse to save Harry, it is clear that nobody suspected that Harry was under an evil curse. So the curse wasn't like Wi-Fi. Since Snape performed a countercurse, not a normal saving spell, he needed to know about the curse in the first place. How did he know about it?

Answer 1

As Snape is a good guy, it's safe to assume that he didn't see Quirrell doing a magic on Harry. Or, he would report that to Dumbledore.

Why is it safe to assume that? We know from Snape's memories in Deathly Hallows that Dumbledore asked him to keep an eye on Quirrell:

Dumbledore turned a page, and said, without looking up, “Keep an eye on Quirrell, won’t you?”
_{Harry Potter and the Deathly Hallows, Chapter 33 - The Prince's Tale}

Unlike the rest of the teachers, Snape has a reason to suspect Quirrell will potentially try to harm Harry. He'd also be in a perfect position to notice any dark magic that Quirrell attempted, because he's keeping an eye on him. Those, combined with Harry's broomstick behaving oddly during the Quidditch match, are I think more than enough for Snape to suspect dark magic rather than a less malicious explanation.

He's also almost certainly going to begin using the countercurse straight away, in order to save Harry, rather than wasting time bringing it to Dumbledore's attention right that second. I would be extremely surprised if Dumbledore wasn't made aware of it afterwards.

Answer 2

When Katie Bell was cursed we see this scene take place.

Professor McGonagall, looking alarmed as she took the necklace from Harry. “No, no, Filch, they’re with me!” she added hastily, as Filch came shuffling eagerly across the entrance hall holding his Secrecy Sensor aloft. “Take this necklace to Professor Snape at once, but be sure not to touch it, keep it wrapped in the scarf!”

Right before this Hermione and Harry state they need to bring the necklace to madam Pomfry, but McGonagall sends it to Snape.

“We need to get you up to the school, sir. . . . Madam Pom- frey . . .”

“No,” said Dumbledore. “It is . . . Professor Snape whom I need. . . . But I do not think . . . I can walk very far just yet. . . .”

“Right — sir, listen — I’m going to knock on a door, find a place you can stay — then I can run and get Madam —”

“Severus,” said Dumbledore clearly. “I need Severus. . . .”

“All right then, Snape — but I’m going to have to leave you for a moment so I can —”

Here we see Snape is who Dumbledore requires when he is under the effects of Dark Magic.

Snape hesitated, and then said, “I cannot tell. Maybe a year. There is no halting such a spell forever. It will spread eventually, it is the sort of curse that strengthens over time.”

Dumbledore smiled. The news that he had less than a year to live seemed a matter of little or no concern to him.

“I am fortunate, extremely fortunate, that I have you, Severus.”

“If you had only summoned me a little earlier, I might have been able to do more, buy you more time!” said Snape furiously.

Through out the whole series we are shown that Snape is exceptional at handling dark magic, knowing counter curses for dark magic ect. So its unsurprising that during the quiditch match over all of the teachers present he would be able to swiftly recognize what was happening to Harrys broom, as well as know what counter curse was needed.

Mcgonnagal or Flitwick could have figured it out as well, but not near as fast as Snape would. And we know Dumbledore was not at this match, as it was unusual he was in attendance in the next match.

Answer 3

From Chapter Eleven of Philosopher's Stone:

"Can't have," Hagrid said, his voice shaking. "Can't nothing interfere with a broomstick except powerful Dark magic – no kid could do that to a Nimbus Two Thousand.

Even Hagrid, with barely three years of magical education, knew that there had to be powerful Dark magic involved. Surely, then, Snape, who was quite accomplished in the Dark Arts, and defense thereof, would know this. If anything, the question should be why the other teachers didn't realize this (we know at least that besides for Snape and Quirrel, McGonagall and Hooch were also present), or if they did realize, why they did nothing about it.

Answer 4

Snape obviously knew that a curse was being put on Harry as he probably knew that the flying brooms don't act that way.

Answer 5

Snape couldn't tell Dumbledore. He was also a Death Eater, so if he tells Dumbledore and takes action, then somebody will find out.

As for the question, Snape knew Quirrell was a Death Eater. It's understandable that Snape would "Keep an eye on Quirrell" (reference to Dumbledore: "Keep an eye on Quirrell, won't you?")