Pithiness is so rarely rewarded, yet I remain a simple man.
In my above post, I forgot to include the condition that the omniscient fellow who instructs the 998 others to scratch off their tickets let you know beforehand that whether or not you had the winning ticket, he would never tell you to to scratch yours off. This is akin to the assumption that Monty never reveals what’s behind the door you already picked. Well duh.
The key to this problem is that Monty knows which door has the prize. The reason this problem is so famous is that people always tell it wrong and confuse others into thinking that Monty opens a random door.