Riddle: Solved by the smartest woman alive – do you get it?

You were asked the following question:
Imagine you are participating in a game show and you have three doors to choose from. Behind one of the doors is a car, behind the other two are goats.
You choose door number one.
The moderator, who knows which door the car is behind, opens one of the doors. For example door number three, behind which a goat is hiding.
He asks you, wouldn’t you rather choose door number two?
Most people see no point in rescinding their original choice. Two doors, a 50-50 chance. Or not?
Marilyn vos Savant’s response: “Yes, you should switch.”
The first door has a 1 in 3 chance that the car is behind it.
According to vos Savant, the probability of the second door is 2 to 3.
How can that be?
Thinking the problem further, with many more doors, it becomes clear why what used to be the most intelligent woman in the world came to that conclusion.
Let’s say we have 100 doors. And choose one.
Then the presenter eliminates 98 doors because he knows there is no car behind them. Only one more remains. do we switch now? Definitely, because at first we only had a probability of 1 in 100. The probability that the car was hidden behind one of the other doors was 99 in 100. Now the presenter has 98 doors, behind which, as far as he knows, goats are removed from the game. This means that the one door he left over now has a probability of 99 out of 100. An unbeatable advantage. The problem is named after host Monty Hall, who hosted a famous game show on US TV.