What's the difference between "think so", and "know so"?

"Is the answer 5?"

"I think so."

"Are you sure the answer is 5?"

"I know so."


"know" is stronger (more certain, confident) than "think".


I believe that "I know so" is only said as a gently mocking answer to "You think so?" "So" is part of the expression "think so", whereas there is no equivalent common expression "know so". So, the conversation would go

"The answer is five."

"You think so?"

"I know so."

 GPY's reply was promoted to an answer.