Look at it this way. You can choose 1 out of 3 doors. Or you can choose 1 out of 2 doors. That's essentially what's going on here. Of course the fewer the doors, the higher chance if success.
Increasing the numbers might help. Suppose you had to pick one out of 1000 doors, then 998 were revealed to have no prize. That might make it more intuitive that your first pick had a lower chance of being right.
Increasing the numbers might help. Suppose you had to pick one out of 1000 doors, then 998 were revealed to have no prize. That might make it more intuitive that your first pick had a lower chance of being right.