The intuitive way to see it is to imagine 100 doors and then all but yours and one other door is eliminated. You almost certainly did not choose the right door

The intuitive way to see it is to imagine 100 doors and then all but yours and one other door is eliminated. You almost certainly did not choose the right door from the outset so your odds are clearly better than 50/50 to switch. The same logic applies to 3 doors.