FAWS comments on Probability puzzle - Less Wrong Discussion
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Comments (26)
That's just Bayesian updating. P(H|E)=P(H)*P(E|H)/P(E)
P(x)=P(H), x=P(E|H), and the integral of the previous step is P(E), since that's the whole point of your probability function.
So that's why it works... I knew it probably tied into Bayes, but I didn't know exactly how.