Please solve this question using theorems and math. For example, bayes theorem. I want to see step by step how the answer is n-1/n mathematically/through theorems.

Problem 5: Conditional Probability Assume you are on a game show, being asked to choose between N doors(N 3). There's a prize behind one of the doors and others are empty. The probability of you choosing the door with the prize behind it is 1/N . Now assume you've chosen a door, but suddenly before opening the door you chose, the host opens N 2 empty doors of the remaining N 1 doors. So now you're left with only 2 unopened doors, the one you chose initially and the remaining one! What is the probability of you winning the prize if you change your decision.