Your wording is fine now, so maybe you already edited it. The key, as JavaFan said, and your post now includes, is that Santa always removes an empty package before giving you the choice of swapping. If he just removed a package randomly, then there would be no point in swapping, because there would be a 1/3 chance that you would be giving up the prize, 1/3 that you would gain it, and 1/3 that Santa would have removed it. Santa is basically allowing you to trade your one package for both of his, while guaranteeing that the prize will be in play. You'd always trade one package for two. It doesn't matter whether he removes an empty one, or trades them both for your one and lets you open both, discarding at least one empty one.

I've had to get out a deck of cards, pulling out a Queen and two Aces, to demonstrate this to people who insisted the odds had to change because the circumstances changed. "Look, let's go through all the possibilities. You're trying to pick the Queen. I deal out Q A A. If you pick the first card, you lose if you switch. But if you pick the second or third card, I discard the other Ace, and you win by switching, so you win 2/3 of the time. Now let's try it with A Q A....." It really doesn't take long, because there are only nine different combinations. Probabilities just aren't taught anymore.