Crash,

Let me try to answer your horse question first.

The assumption is that all 10 runners have equal chances.

The chance of your 3 picks filling 1st, 2nd and 3rd in any order is the spreadsheet expression:

=1/combin(10,3)

=1/120


The Peter gamble is actually a variation of the infernal St Petersburg Paradox. I only found out about that today, and I'll comment if I can work my way through it.