I abandoned my cleaning materials and went after them. Slowly and steadily, making sure that they weren't able to hear any of my footsteps.

If they saw me following them, would they not notice that something was wrong?

They might be fools, but it was possible that they were not complete fools without any sense.

After they opened the door leading to the stairs, I passed through the door also, before I halted in a corner and watched them.

Well, I stood in a corner and watched them after ...