It's not simple. :/
Do you think it's as simple as 1/5 is better than 1/6?
If she picked 2 and now 6 gone, her pick is still 2, which is 1 out of 5 possible eggs, changing it to 5 wouldn't do anything, it's just another of 1/5 possible eggs.
If 6 is gone, egg 2 doesn't become less likely to win.