That's a fair question, but we're in danger of conflating two different concepts. Knowledge is the information, and belief is the action. It's a little bit like having money vs spending money. You can have money, you can spend money, and you can have spending money, and you can spend money you don't have. These are all slightly different concepts despite using the same words.

When you think you know something, but you are mistaken, we call that a "belief" even though you did not doubt it. You believe you know something without a doubt, but you are wrong. You do not know, and you should doubt your belief. But you would never describe it as a belief, because you do not believe you do not know for certain.