Perhaps you're just kidding around, but of course that's not good enough for a definition. It doesn't handle continuous random quantities. It doesn't even hand

Perhaps you're just kidding around, but of course that's not good enough for a definition. It doesn't handle continuous random quantities. It doesn't even handle situations with a discrete outcome but where counting the possible cases isn't well-defined (Buffon's needle being one, but an even better one being the chance of a tossed thumbtack landing point-up). It also doesn't handle cases where symmetry or physics can give the answer, but you can't count cases because they aren't finite or aren't necessarily a-priori equiprobable.