You are on a game show where you can win a car that is hidden behind one of three closed doors. Behind each of the other doors is a toy car. You pick Door #$3.$ The host then opens Door #$1$ to show you that it contains a toy car and asks if you want to keep your original door or pick Door #$2.$ Should you switch to Door #$2?$ Why or why not? Support your stance using the concept of probability.