The Prisoner's Problem

From Judea Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. 1988 Morgan Kaufmann.

There are three prisoners, A, B, and C. Exactly one of them is scheduled for execution to-morrow. The other two are to be given pardons. Only the Governor knows which prisoner is to be executed. A, thinking correctly that at least one of his friends, B and C are going to be pardoned, offers the following proposal to a nearby guard: "Go to the governor and find out which one of us is to be executed. Then, deliver a message to just one of my friends, B or C, letting him know that he will be pardoned." The guard agrees, and returns later and says that he gave the pardon message to B. Given all of this, what are A's chances of being executed?