Your friend places 100 cards face down in a row; exactly one of them is the…

Your friend places 100 cards face down in a row; exactly one of them is the Jack of Clubs, and you need to guess which one it is. You pick the card at position 15. The host knows exactly where the Jack of Clubs is: he will never remove the card that holds it, and if your own pick already holds the Jack, he chooses which other card to leave uniformly at random from the remaining 99 cards. He now removes 98 of the remaining 99 cards, leaving only your chosen card at position 15 and one other card at position 87, and says, "One of these two cards is the Jack of Clubs." What is the probability that the card at position 87 is the Jack of Clubs?