Who believes Tom Robinson has a chance at being set free? Why do they believe this?

“Aw, Atticus, let us come back,” pleaded Jem. “Please let us hear the verdict, please sir.”

“The jury might be out and back in a minute, we don’t know—” but we could tell Atticus was relenting. “Well, you’ve heard it all, so you might as well hear the rest. Tell you what, you all can come back when you’ve eaten your supper—eat slowly, now, you won’t miss anything important—and if the jury’s still out, you can wait with us. But I expect it’ll be over before you get back.”

“You think they’ll acquit him that fast?” asked Jem.

Jem is still young enough to believe his father can overcome anything because he does the right thing. He's in for a disappointment.