I believe 0 and 1 are probabilities, but there is no way to obtain that degree of certainty. (unless you have an incredibly clever method you aren't sharing, which is mean)
An analogy would be that I believe that 3^^^3 is a number, even though I don't think I will ever have that many dollars. Similarly, I believe that 0 and 1 are probabilities, but I wouldn't grant any particular belief a probability of 0 or 1.
My intention was to make a stronger claim than the one you agree with, but fortunately my degree of confidence takes care of that for me.
I was very interested in the discussions and opinions that grew out of the last time this was played, but find digging through 800+ comments for a new game to start on the same thread annoying. I also don't want this game ruined by a potential sock puppet (whom ever it may be). So here's a non-sockpuppetiered Irrationality Game, if there's still interest. If there isn't, downvote to oblivion!
The original rules:
Enjoy!