Conditional Probabilities with Higher-Order Intersections Question

A man has *n *keys on a key ring, one of which opens the door to his apartment. Having celebrated a bit too much one evening, he returns home only to find himself unable to distinguish one key from another. Resourceful, he works out a fiendishly clever plan: He will choose a key at random and try it. If it fails to open the door, he will discard it and choose at random one of the remaining *n-1* keys, and so on. Clearly, the probability the door opens with the *third* key he tries is also 1/*n*. (Hint: What has to happen before he even gets to the third key?)