What do you mean "personally" ? Are you expecting a process to behead the Prime Minister or something ?

The Government led by that person falls. Parliament can in principle pick a new government, but in practice is likely to trigger a General Election instead and replace all the MPs. Since the Prime Minister is chosen by those MPs, the new one even if it's the same person, clearly does have their confidence, at least for now, right ?

Anyway, even when the PM survives a confidence vote that's often bad for them, if some of "your" people vote "No confidence" (as must happen for a Majority government) or even if those who've promised Confidence to you (in a Coalition) actually renege, you're done even if you carry the day in the House. This is also true for internal processes. You can, and often Tory PMs do, win a 1922 committee vote and then resign by next week because you'd expected to win by a huge landslide and instead it turns out dozens of people you'd thought were solid have doubts after all.