Would you fold AA here?

This is totally hypothetical, but I'm interested in the responses.

Here's the situation. It's a low level STT, 4 people left, top three payout, and blinds are 200/400:


Player A has like 7000 chips
Player B has 2400 chips
Player C has 2000 chips
You have 400 chips

Say that you're small blind, so you're down to 200. Player A is big blind. Player B goes all in, and Player C calls. You have AA. Do you complete the blind and go all in?

The way I see it, Player B and Player C are about 50% each to win, right? If B wins, you're in 3rd. If C wins, then B, who is in the big blind next hand, will be forced to win. We'll say he has a 50% chance of winning the following hand if he loses this one. This means you have a 75% chance of getting 3rd, right? But if you don't call, you'll pretty much be forced into 3rd unless there's some kind of fluke. If you call and WIN, you'll have 1200 vs. stacks of 7000 and 4400, giving you say a 15% or so chance of making it to 2nd or 1st. However I don't think AA is 75% against two random hands.

So how would you play it? I'm curious to see peoples answers on this (personally I would fold, but I'm a wuss).