A priori probabilities are probabilities that you can calculate before conducting experiments, using thought alone.
If I were to presuppose a 12-sided die, you could calculate (without much trouble) the probability of my rolling a 1. Of course, this calculation would assume certain things -- that the die was a true dodecahedron, and that all sides were weighted equally. We would not have to do any actual testing of 12-sided dice to have confidence in this prediction. We might even start with our a priori probability prediction and use it to test the quality of any 12-sided we come across -- roll the die 10,000 times, and the closer it comes to rolling a 'one' 833 times, the more confident we are that it is a well made and even die.
If we wanted to find my chances of being struck by lightning, we'd do best to avoid a priori probability, and go with a posteriori statistics instead.
Similar in concept to a gedanken experiment.