In a great book “Stalking the Black Swan”, the author, Kenneth A. Posner, writes an anecdote illustrating conditional probability.

"This brainteaser makes the point that the diagnostic power of an answer depends critically on how you ask a question. (It is adapted from a book on probabilistic reasoning by Judea Pearl, a researcher in artificial intelligence).

Three prisoners-A, B, and C-have been tried for murder, and their verdicts will be revealed in the morning. One of them will be found guilty and hanged, whereas the others will be released. Their guard knows which of the prisoners is guilty. But the prisoners do not.

In the middle of the night, prisoner A calls the guard over and asks, "Please give this letter to one of the other prisoners to take home to my family in case I am executed. We both know that at least one of them will be released." The guard agrees.

An hour later, prisoner A calls the guard again and asks, "Can you tell I me which of the other two prisoners you gave the letter to? The answer won't give me any clue to my own fate." The guard agrees and reveals that I he gave the letter to prisoner B.

Upon hearing this answer, prisoner A becomes alarmed, reasoning that the guilty sentence now falls with equal likelihood on himself or prisoner C. Before asking the question, he had thought that his own probability of being executed was one-third. Now it seems to be 50%.

But in fact this is wrong. The probability of A’s execution remains one third, because the question has no diagnostic power with regard to A’s fate: no matter which prisoner is the unlucky one, the guard can always give A’s letter to one of the other two prisoners, so A really learns nothing new about himself. What changes in this story is the probability of C being executed, which rises from one-third to two-thirds, because the guard did not give him the letter.

Prisoner A could have learned more about his own fate had he asked the guard a different question, such as, "Will prisoner B be executed tomorrow?" If the guard said "Yes," then the probability of A suffering that fate would drop to zero, since only one prisoner will be executed. If the guard revealed that B would go free, then A would realize that his own odds of being executed were indeed now 50% (split equally between himself and C).

How you phrase a question may determine whether the answer provides information relevant to your particular set of critical issues-or to other variables."