If you draw n realizations from U(0,1), then will the sorting of those values (on average) be separated by $\frac{1}{n+1}$ between two consecutive values. E.g., if n=5, then the lowest one is realized at 1/6, the second lowest one at 2/6 etc.
Furthermore, could I take the above values (1/6, 2/6..., 5/6) set them equal to the c.d.f. of any other distribution, then solve for x (five values in total), and it will yield the order statistics for n=5 values for that the new distribution?
I'm only using intuition here, so my gut feeling might be wrong. The stuff I've read online is too technical for me.