Answer: Switch doors

Original probability of  car behind your door: 1/3

Original probability of car behind other two doors: 2/3

If host eliminates one of the two doors (he knows which does not have the car) the probability of the car behind the door is still 2/3.  Hence, you double your chance of winning. 

Think of it this way:

Probability of your door winning is 1/3

Probability of the other two doors is 2/3

If you could pick the other two doors “together” you have a 2/3 probability of getting the car.  The host eliminates a goat from these two.  Your probability is still 2/3.

Another way of looking at it:

Your probability of winning is 1/3

Probability of the other two doors is 2/3

One door is eliminated.  Your probability is still 1/3.  Probability that it is the other door is 1-1/3 = 2/3  because probability must equal 1.