There are several reasons why we might assume that Jem is convinced Atticus will win the case. The author is successful in conveying the deep admiration Jem has for Atticus. He aspires to be like him (including becoming a lawyer) and never wants to disappoint him. The fact that he admires Atticus so much makes him convinced of the fact that he is going to win.
Moreover, Jem has a strong sense of justice. He believes in the good of the world, and once he understands that the "just" outcome would be for Atticus to win, he is convinced this is what will happen. The realization that justice does not always work is one of his most significant transformations.
Finally, the author conveys the sense of despair that Jem feels when he hears the verdict. He is ready to get rid of juries altogether, and seems to never want to hear about the courthouse again. This shows that the outcome was an unexpected and very unpleasant surprise to him.
