Same process in Poland (start by enrolling anywhere, later exams from the previous school matter), yet the difference was big. High schools in my home town got between 98% and ~10% people advancing higher. I guess 98% wasn't 100 because kids moving to schools abroad were counted as "not on the list of local universities".
For primary school you pretty much started in a mixed, local group, without any visible bias, so chances were really very similar for everyone.
I would argue that it's more because of self-selection, not because of good schools being that good:
Those who have the motivation and background to continue to higher education also tend to shift towards "good" schools. They would continue even if they didn't go to a "good" school.
For primary school you pretty much started in a mixed, local group, without any visible bias, so chances were really very similar for everyone.