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nshepperd comments on Inherited Improbabilities: Transferring the Burden of Proof - Less Wrong
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Yes.
P(Guilt|A) = P(A|Guilt) only when P(A) = P(Guilt). In which case it would be 100% proof. But that is a rare situation.
Nitpick: the two conditionals also be equal if A and Guilt were mutually exclusive. (in that case, of course, the two conditionals would be both zero)