Is it safe to say that this problem, this result, has no applicability to any similar problem involving a merely finite amount of prisoners, say a mere googol of them?
Yes. But I do think that thinking critically about the assumptions you are making, in particular that you can meaningfully talk about what it means to pick a random individual in a uniform fashion, is worthwhile for understanding a fair bit of probability and related issues which are relevant in broader in contexts.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.