conditional probability and Bayes

Bayes is most used to know probability backwards.
Supose we are at the car races and there are 10 cars.
The chance to pick the winner is 1/10.
But, we know that driver 1 and driver 2 have some hidden conditions.
Driver #1 is has more experience and driver #2 has done some improvements in his engine.
Supose, driver 1 wins and driver 2 gets the 2nd place.
How do you calculate probabilities with Bayes?