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...

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?