Imagine you have to guess a random number between 0 and 255, i.e. you have to guess 8 bits. You already know that it's less than 128 so the most significant bit is 0. Can you derive any knowledge about whether the second bit is 0 or 1?
Instead: Make a sample and now you know that it is greater than a random number unknown to you. Can you derive any knowledge about your next sample?
There's two coins on the table that you don't see. The only information provided is that
a) one of them is tails b) the left one is tails
What is the probability of both being tails?
It's 1/3 in (a) and 1/2 in (b). The reasoning being:
1. At first both HH, HT, TH and TT are all equaly likely. 2. In case (a) we discard HH as an option, but in case (b) we discard *both* HH and HT.