Question: The winner of this year's No-Bull prize is about to be announced. The finalists are Danny, George and Sam. Danny believes that exactly one of them will win. Furthermore, Danny believes that he has a 10 percent chance of winning and that Sam is twice as likely as George to win. In order to build suspense, the announcer is going to call out the names of the two finalists who didn't win before naming the winner, as in the example: "The second runner-up is X, the runner-up is Y, and the winner of the No-Bull prize is Z."
Danny believes that the announcer is equally likely to name either George or Sam first if Danny himself is to be named the winner. Then Danny happens to overhear a conversation between the announcer and a previous No-Bull prize winner, Maggie, and learns that the announcer will name George before Sam. Now what probability does Danny assign to himself being the winner of the No-Bull prize?