You participate in a game show where you must choose between 3 doors. Behind 2 doors is a goat, but behind 1 door is a car. You pick a door, say door no. 1, but before you open the door, the host opens another door, say door no. 3, which has the car behind it. "Oops," says the host.
You lose.
I think, for me, the easiest way to visualize this is this.
1 )Instead of 3 doors, you have, lets say 10.
You first pick a door. You have a 1/10 chance of been right the first time. This chance doesn't change at all.
Host eliminates 8 of the remaining doors with no car, leaving just 1. We are back the "50/50" situation, except its not truly 50 /50. Your initial chance of 1/10 has not changed.
Ask yourself this - Do you stick with your initial chance of 1/10? He already removed 8 bad choices for you. Remember the host knows where the car is always. Given the new information, you should definitely positively switch.