Preventative Medicine for Gamblers: The Powerball Paradox

The lottery paradox is as follows: Say I buy one Powerball ticket and there are 10 million tickets sold.  Furthermore, let's imagine that we know that one of the tickets is the winning ticket (of course, this is not be true of the Powerball since it is possible that none of the tickets is the winning ticket - that's what gets us the rollover). The chance of my ticket being the winning ticket is one in ten million - poor odds by anyone's estimation. It appears rational to think that one should believe a statement to be true if and only if one is sufficiently confident in the statement being true. So, one would think I would be fairly rational to say the following: "my ticket is not the winning ticket." 

Here's the problem: if it is rational to say that my ticket is not the winning ticket, it is rational to say that all ten million tickets are not the winning ticket. If it can be said about Ben's ticket then there is no reason why it shouldn't be said about the tickets belonging to Jill, Albert, Aunt Violet and everyone else. But then there's a problem: we already know that one ticket is the winning ticket. 

So, I have a challenge for you: before you play Powerball you have to solve the paradox. Hopefully, this will prevent you playing it at all.