Let's suppose we are doing a computer simulation.

1. We simulate a million trials where the contestant chooses one of three door, one of which has a car and two a goat

2. We simulate the host randomly choosing one of the remaining doors to open.

3. We discard all trials that resulted in a car. We are left with the number of trials that resulted in a goat and store that number in a variable 'total'

4. In the remaining trails we switch and reveal what was behind the door. We store the number of times we saw a car in a variable called 'wins'.

5. The probability of winning after switching is 'wins' / 'total'

It doesn't matter how many times the host shows a car because those trials are discarded.