Three convicts A, B, and C know that the warden has randomly chosen one of them

Question

Three convicts A, B, and C know that the warden has randomly chosen one of them to be
shot at dawn. Convict A is, naturally enough, curious to know whether he was selected.
He realizes that the warden would refuse to answer the direct question "Am I to be shot?".
However, since either B or C is to be spared in any event, he believes that the warden would
consent to name one of the other prisoners who was to be spared. He asks, and the warden
tells him that C is to be spared. Convict A goes away very unhappy. Before he asked, he had
only one chance in three of being shot, but now he knows C is to be spared, and his chance
of being shot has risen to 50%. Do you agree with his reasoning? Find the probability that
he is the one to be shot given the warden's answer.
Note: Assume that, if both B and C are to be spared, the warden chooses the one he names
at random.

Explanation / Answer

Initially the warden had chosen randomly one from three. So all are equally likely to be selected. When warden said C will be spared then A and B are equally likely to be selected. So probably that A will be selected is 0.5

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