thought on monty hall problem

i originally think that staying at my choice have better chance to win, but now, switching have 2/3 chance of winning compared to staying which only 1/3.

One interesting thought:

Let say between Abd, Anw and Naj , one of them is the "car" , which can truly lead the country. Now , we have choosen Abd. By some mean , the host ( god or Allah or whatever) , open another door Naj and show goat behind( indicate Naj is not the car) . So does switching to Anw lead a better chance to win the car ( a better leader)?
interesting, isn't it?