Here is yet another explanation of the answer.
It requires tables and color. 
Some other pages The WWW Tackles The Monty Hall Problem Monty Hall Problem Three Door Puzzle Monty Hall Problem 
There are 3 doors

So the universe is in one of 3 possible states
 
Now, you choose a door.

Looking inside, we see P in just one of the 3 possible states.
But if it is in state2 or state3, we don't. Our chances are 1/3 for "P", and 2/3 for "".  
Now "Monty" takes the other two doors

and opens one without the prize
Now which door do you want, red or green?
If the universe is in state2 or state3, we get the P. Only if it is in state1, do we lose. So our chances are 2/3 for "P", and 1/3 for "".  

Notes: A friend called to ask about the Monty Hall Problem. I liked this explanation, but it didn't work over the phone. Not seeing it already online, I wrote this. This presentation is similar to this Answer to the Monty Hall Problem, but sufficiently different that I went ahead with this one anyway. Doables: History: 1998.Oct.15 Created.