The probability of drawing a high numbered ball from the million ball urn is zero if the person filling the urn has had only enough time to put in the first ten balls. Drawing a seven tells us nothing about how many balls will eventually be placed in the urn. For the experiment to work, I'd have to wait until all of the balls are placed.

Even if the human race will be much larger, we haven't been around long enough to produce trillions of members so of course my birth order is low. No matter how large the population will become, everyone doing the experiment now is going to get a low birth number. It has nothing to do with how large the population will become just as the early drawing of a ball from an urn doesn't tell us how many balls will eventually be placed in it.

It may be true that most of the people from among everyone who will ever live will be correct in guessing that the human race will become extinct soon, but I have no reason to believe that I'm in that majority because we're not done producing more people. A ball can't be drawn from an urn if it hasn't been put in yet.