The belief that the children hold that the Professor could not be the murderer is based both on instinct and on wishful thinking. April is the only one of the children involved in the Egypt game who has actually ever spoken to the Professor in person. When she met him in his shop, she found herself prattling on and telling him things about herself that she normally wouldn't tell an adult stranger. April states more than once that she is good at reading grown-ups, and even Melanie believes April is pretty adept at understanding adults, even if she's not so good at understanding kids her own age. Because April has pretty reliable instincts about grown-ups, and because she found herself opening up to the Professor, she doesn't think he could be guilty of the unsolved murders.
The other children follow April's lead, as they do for much of their game. Beyond that, however, they simply don't want it to be true that the Professor could be a killer. Obviously, if he turned out to be guilty, that would put an end to the Egypt game. No one would want to play in the backyard of a brutal criminal. Because they believe the continuation of their game depends on the Professor's innocence, they engage in wishful thinking, convincing themselves that the Professor could not be the killer.
Because of their instincts and because of wishful thinking, the children refuse to entertain the possibility that the Professor could be the unknown killer.