I'm reading Chapter 5 of the CLRS Algorithms book. Specifically, it discusses the hiring problem in which we want to assess the expected number of hires given that candidates arrive in random order and each candidate has a distinct rank. All permutations of candidates are deemed equally likely.
As an example of what's deemed a 'hire', let's say candidate 1 has rank 5 and candidate 2 has rank 10. Since candidate 2 has the highest rank seen so far, candidate 2 is hired. In order for a candidate to be hired, it needs to thus have the maximum rank of all ranks seen up until that point.
The book states "Because we have assumed that the candidates arrive in a random order, the first $i$ candidates have appeared in a random order. Any one of these first $i$ candidates is equally likely to be the best-qualified so far".
I know this sounds trivial, but why does random order over all $n$ candidates guarantee random order over the first $i$ candidates? Intuitively, it seems to make sense but I can't explain it formally and thus don't feel like I really understand it.