Every option of computer lottery is a probability of 1/3, and the first one is A. There is no doubt that the probability of A winning is 1/3, so there will be two situations after A draws a lottery: 1 and A winning. 2.a didn't win the prize. The probability of 1 is 1/3.
It's a very fair choice mode for everyone that you can't choose one-on-one lottery mode. You don't have to worry about or argue about the order of lottery, and it won't affect the results one by one.