My response is here, a post on my blog from last August.

Basically when Bob sees Alice present the particular sequence, he is seeing something extremely improbable, namely that she would present that individual sequence. So he is seeing extremely improbable evidence which strongly favors the hypothesis that something extremely improbable occurred. He should update on that evidence by concluding that it probably did occur.

Regarding the lottery issue, we have the same situation. If you play the lottery, see the numbers announced, and go, "I just won the lottery!" you are indeed probably wrong. Look again. In most cases you will see that the numbers don't quite match. In the few cases where they do match, you are seeing extremely improbable evidence that you won the lottery, namely that your numbers match after repeated comparisons.