A puzzle

[Googolplex]

You are in a show and you can win a car. The car is located behind one of three doors. The other two doors are empty. You have one choice. After you told the showmaster which door he should open, he just opened an other door which is empty and makes you a suggestion: "Now, there are only two doors remaining. You can now stay at your first choice or switch to the other possible door."

Makes it sense to switch? Or doesn't it matter?

And then an other candidate comes to the show and has to choose between the two remaining doors. He doesn't know that there's already one door omitted and he doesn't know your choice. But he chose the same door like you. Does he has the same prospects to win the car?