A prisoner wakes up in an empty room (being seated on the floor against the wall). There are three solid doors on three of the room's walls: one to his left, one in the middle in front of him and one to his right. The fourth wall behind him) is a thick glass pane with an intercom built in.
Through the intercom the warden says: "One of these doors leads to freedom, the other door [note the singular] leads to death. You may choose one door for me to unlock. You may ask me two questions which I will answer with 'yes' or 'no' to help you choose." (but not "maybe" or any other third value: in that case, the answer will be "no".)
The prisoner is confused and hence asks: "What's behind the third door?" [b]
The warden answers: "No, I can't tell you, because that's not a yes-or-no question. It still counts as your first question though."
The prisoner complains: "That's unfair!"
The warden responds: "No, it isn't, you don't even need that second question to survive."
After some contemplation the prisoner asks his second question, chooses a door and goes free.
- what question did the prisoner ask and what was the answer?
- what was behind the third door [a] and what was the probability for the prisoner to pick it?
(If multiple valid solutions the one with lowest probability for the third door wins.)
[a] Hint: as some already noticed, the third door leads back to prison (the prisoner had to be brought into the room in some way, after all), hence leads neither to death nor to freedom.
[b] Note: after to the prisoner's first question, the warden knows that the prisoner doesn't know what is behind the third door - but the warden knows that the third door leads back to the prison.