Suppose you don't win the prize for the first time, its probability is 2/3. At this time, if you change your choice, the probability of winning is 1, and if you don't change your choice, it will be 0.
To sum up, the winning probability of changing the choice is (1/3) × 0+(2/3 )×1= 2/3.
The winning probability is (1/3 )×1+(2/3 )× 0 =1/3.
In other words, the probability of winning the prize by changing the choice is greater, which is 2/3.