A king announces to release two out of three prisoners (A, B and C) and execute

Question

A king announces to release two out of three prisoners (A, B and C) and execute the third one, but keeps their identities secret. One of the prisoners, prisoner A, considers asking a friendly guard to tell who is the prisoner other than himself that will be released. However, he hesitates because of the following rationale: Based on his present state, his probability of being released is 2/3. But if he knows the answer, the probability of being released will become 1/2, since there will be two prisoners (including himself) whose fate is unknown and exactly one of the two will be released. What is wrong with prisoner A's argument?

Explanation / Answer

if B and C are are releasing then there is a probability of '0' being released. he is missing it in his question, where he is thinking that he will be released.

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