This is a twist on the well-known Monty Hall problem. If you aren’t familiar with this, solve this first.
The rules are the same as ever: there are three doors, behind one of which is a car, with only goats behind the other two. The host knows which is which, but I do not; I will pick a door, and then the host opens a door other than the one I picked to reveal a goat, before offering me the chance to change my choice to the one remaining door. This time, when I am walking up onto the stage, I notice that exactly one of the three doors smells faintly of petrol: I estimate that the probability of a door smelling of petrol, given that the car is behind it, is , while the probability of a door smelling of petrol, given that a goat is behind it, is .
In light of this new information, what is my best strategy?