As a reader, we know many things that other characters don't know, such as Harry being a Parselmouth (until revealed). Before a Quidditch match (or practise), Hermione becomes very enlightened to a idea regarding the Hogwarts' monster.
In the second novel, the following is found:
“Harry — I think I've just understood something! I've got to go to the library!” And she sprinted away, up the stairs. “What does she understand?” said Harry distractedly, still looking around, trying to tell where the voice had come from. “Loads more than I do,” said Ron, shaking his head. “But why’s she got to go to the library?” “Because that’s what Hermione does,” said Ron, shrugging. “When in doubt, go to the library.”
It seems more than just a guess, but something very factual. What triggered Hermione to become so definite?