The floor of the entrance is exactly at the right height, a little to the right of a crucial element to get access to the upper chambers: The crossing between the ascending and descending passage. This is where the ascending passage was blocked - you can see one of the large granite blocks still in place today. The (presumably) robbers goal was to get behind those granite blocks. This passage leads straight on to the crossing, then taking a sharp left turn just right behind the blocking. Whoever built this path must have known where it should lead to. That makes the story that Al Mamun did it so unlikely. He might have enhanced an existing tunnel, but there is no conceivable reason why he should have built it in the first place. Here is a rough illustration, the dark brown being the robbers tunnel: http://www.benben.de/Architektur/Cheops/Grafik/Mamun3.jpg