Chef and An Ideal Problem

"An ideal problem has no test data." - aryanc403 **This is an interactive problem.** Chef likes probability puzzles a lot, almost as much as interactive problems. Today, he learned about the Monty Hall Paradox. Suppose that Chef is participating in a game show, where he has to choose between three doors numbered $1$ through $3$. There is a car behind one of the doors and goats behind the other