= Three prisoners problem
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A messenger names an excluded candidate while concealing the uniquely selected one. The <conditional probability> depends on the naming rule. With three equally likely selected candidates and a messenger forbidden to name the observing candidate A, let $s$ be the probability of naming B when A is selected. When C is selected the messenger must name B, and when B is selected cannot name B. Thus the probability that A is not selected, conditional on B being named, is $1/(1+s)$. Unbiased naming has $s=1/2$ and leaves this probability $2/3$; bias toward B gives $1/2$, and bias toward C gives one. Conditioning on the name is different from conditioning only on B's exclusion.
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