囚犯假释：问“另一个会被释放的人”会改变概率吗

Three prisoners, $A,B$ , and $C$ , with apparently equally good records have applied for parole. The parole board has decided to release two of the three, and the prisoners know this but not which two. A warder friend of prisoner $A$ knows who are to be released. Prisoner $A$ realizes that it would be unethical to ask the warder if he, $A$ , is to be released, but thinks of asking for the name of one prisoner other than himself who is to be released. He thinks that before he asks, his chances of release are $\frac{2}{3}$ . He thinks that if the warder says " $B$ will be released," his own chances have now gone down to $\frac{1}{2}$ , because either $A$ and $B$ or $B$ and $C$ are to be released. And so $A$ decides not to reduce his chances by asking. However, $A$ is mistaken in his calculations. Explain.