The statement "That prisoners 5 to 8 will also find their numbers can also be derived from the information gained by the first three prisoners" is poorly worded

The statement "That prisoners 5 to 8 will also find their numbers can also be derived from the information gained by the first three prisoners" is poorly worded. I think the author intended it to mean the information gained to you, an outside observer trying to prove this statement. There is no transfer of information from one prisoner to the next. Also, when the prisoners find their number they don't remove it. No drawers are ever empty. They just have to open a drawer that contains their number.