Conditional Probability, Independence & Bayes · Challenge problem

One of three prisoners $A$, $B$, $C$ is to be pardoned, chosen uniformly at random. Prisoner $A$ asks the guard to name one of the other two who will be executed; the guard (choosing uniformly between them when free to) truthfully names $B$. Find the probability that $C$ is the one pardoned.

Express your answer as a common fraction.