If Alan found the car the game continues. Becky then
Opens A, finds the car (p=1/3), then finds the keys behind either B or C (p=1/2). Overall P=1/3 x 1/2 =1/6
Opens A, finds the keys (p=1/3).
Opens A, finds the goat (p=1/3) but then knows the keys are behind B because Alan opened C and found the car.
So overall probability for Becky is 1/6 + 1/3 + 1/3 = 5/6.