Harry ruffled a hand through his own hair. Maybe it was just that strange part of him which had already been convinced, but... "That's a bit of an anticlimax," Harry said. "You'd think there'd be some kind of more dramatic mental event associated with executing a Bayesian update on an observation of infinitesimal probability -" Harry stopped himself. Mum, McGonagall, and even his Dad were giving him that look again. "I mean, with finding out that everything I believe is false."
By Less Wrong, Harry Potter and the Methods of Rationality. Petunia married a proper Skeptic (or Sceptic, in British!) and Harry knows about Feynman and the scientific method and proposes a test of Professor McGonagall worthy of James Randi and... yeah.
It's not a complete fic, but it's an absolute treasure.