Yes, that's the prior probability, before you observe the first outcome. This is a common gamblers' fallacy; past events do not affect future events from which

Yes, that's the prior probability, before you observe the first outcome. This is a common gamblers' fallacy; past events do not affect future events from which they are independent! I'm assuming that you and/or the GP are assuming that everyone can win and everyone's ticket has a random digit drawn separately. However, if we assume that you know what number you picked, you don't know the result of the lottery, you know that the person in front of you won, and he chose his digit uniformly at random, the probability is still 1/10, because it has already been decided that he and the lottery chose the same digit.