The contestant picks a door and Monty opens one of the remaining doors, one he knows doesn't hide the car. If the contestant has already chosen the correct door, Monty is equally likely to open either of the two remaining doors.
After Monty has shown a goat behind the door that he opens, the contestant is always given the option to switch doors.What is the probability of winning the car if she stays with her first choice? What if she decides to switch?
Direct quote from The Math Forum Ask Dr. Math: FAQ