I really don't know the probability of a person saying hello to a stranger who said hello to them. It depends on too many factors
I'm not asking for the probability. I'm asking for your probability -- the confidence you have that the event will occur. If you have very little confidence one way or the other, that doesn't mean you assign no probability to it; it means you assign ~50% probability to it.
Everything in life depends on too many factors. If you couldn't make predictions or decisions under uncertainty, then you wouldn't even be able to cross the street. Fortunately, a lot of those factors cancel out or are extremely unlikely, which means that in many cases (including this one) we can make approximately reliable predictions using only a few pieces of information.
but if there were not a time constraint, I think Deep Blue's moves would be almost 100% predictable.
Without a time constraint, the same may be true for the girl (especially if cryonics is feasible), since given enough time we'd be able to scan her brain and run thousands of simulations of what she'd do in this scenario. If you're averse to unlikely hypotheticals, then you should be averse to removing realistic constraints.
A stub on a point that's come up recently.
If I owned a paperclip factory, and casually told my foreman to improve efficiency while I'm away, and he planned a takeover of the country, aiming to devote its entire economy to paperclip manufacturing (apart from the armament factories he needed to invade neighbouring countries and steal their iron mines)... then I'd conclude that my foreman was an idiot (or being wilfully idiotic). He obviously had no idea what I meant. And if he misunderstood me so egregiously, he's certainly not a threat: he's unlikely to reason his way out of a paper bag, let alone to any position of power.
If I owned a paperclip factory, and casually programmed my superintelligent AI to improve efficiency while I'm away, and it planned a takeover of the country... then I can't conclude that the AI is an idiot. It is following its programming. Unlike a human that behaved the same way, it probably knows exactly what I meant to program in. It just doesn't care: it follows its programming, not its knowledge about what its programming is "meant" to be (unless we've successfully programmed in "do what I mean", which is basically the whole of the challenge). We can't therefore conclude that it's incompetent, unable to understand human reasoning, or likely to fail.
We can't reason by analogy with humans. When AIs behave like idiot savants with respect to their motivations, we can't deduce that they're idiots.