Evens perhaps, not that unlikely. First draw doesn't count towards the calculation, it could be any. Second draw in the pot there is one the same as the first and 2 different, so it's a 2:1 on chance you get a different one. Third draw there are 3 in there 2 of which have been drawn before, so it's 1:2 against drawing a different one. If you went to a fourth draw you would be bound to get a winner, but there is no point in that, you might as well just draw it once and go with the first choice.
Or allocate each choice a number and put a formula in a cell in excel, from memory it would be something like =1+(int(Rand*3)) , that would give you a random whole number between 1 and 3. (I would need to check that formula, not got Excel in front of me right now).
Another decision making method which is not at all random is the 3 chairs method. Sit in a chair, relax, imagine yourself one year in the future. Picture yourself out on a walk calling your dog. "Come here Persephone" or whatever. How does that make you feel? Now go to another chair, repeat with another name, then a third. Eliminate one, repeat. Works for me.