Yeah, looking at it with Bayes rule makes it sound more convincing. Here's what's assumed: * The guard can't express whether or not A was pardoned to A. * The

Yeah, looking at it with Bayes rule makes it sound more convincing. Here's what's assumed: * The guard can't express whether or not A was pardoned to A. * The guard is telling the truth. Then the named (named to prisoner A) executed person E must be either B or C if A is saved. Let the saved person be S. Then: P(S=A|E=B) = P(S=A) P(E=B|S=A) / sum_{S in {A, B, C}}(P(S) P(E=B|S)) = P(E=B|S=A) / (P(E=B|S=A) + P(E=B|S=B) + P(E=B|S=C)) = P(E=B|S=A) / (P(E=B|S=A) + 0 + 1 ) As mentioned in the OP, if S=B then E=C and if S=C then E=B necessarily: both these events happen with equal probability. Then, as you mention with your intuition, if, say, the guard prefers to name B in the case of S=A, then hearing that E=B really does give you some information, since there is more probability mass in situations where you're saved when looking at the subset of events where E=B. Put extremely, taking P(E=B|S=A) = 1, we find that indeed P(S=A|E=B) = 1/2!