The first time I recall encountering this argument was in Alan Moore’s Watchmen, where the probability of the what you describe is likened to “events with odds so astronomical they’re effectively impossible, like oxygen spontaneously becoming gold”. Even then the argument didn’t sit right with me.
I find itthe argument similar to the gambler’s fallacy. An example:
In a fair coin toss, the probability of landing on heads (or tails) is 50%. Before we start tossing the coin, how likely do you think it is that the coin will land 20 consecutive times on heads? As you’d expect, they are astronomically low. Also as expected, while making the calculations every consecutive toss we add lowers the probability — landing 10 consecutive heads is less likely than landing on it twice.
But now let’s say we’ve already made 19 tosses that all landed heads. What’s the probability the next toss will also land on heads? The gambler’s fallacy is thinking the previous math applies and the odds are astronomically low. They are not — they are once again 50%. This is because the coin doesn’t care how many times it landed on the same side. It’s not self aware and won’t try to “correct” itself to (what we call) a fair/balanced result. Every toss is statistically independent from another, individually they all are 50/50. Looking at past tosses gives us no information of future results. Statistics apply when the tosses we want to predict are all in the future.
The same happens here.
If centuries ago one asked “what’s the probability of the specific person R_K being alive on the specific time of June 17 2018”, the odds might indeed be astronomically low. But no one asked that question, so the fact you’re alive at this moment is as (ir)relevant as you being alive at any other point in history. They’re all as probable as you having never existed in the first place. If you (or me, or anyone else) had not existed, no one would have known or cared. You are a person, some person, not the specific person someone else was predicting or waiting to exist in a point in time.