Have you seen Knight-Knave puzzles based on probability rather then facts?
For example a puzzle with condition like this: Knight tells the answer, probability to which according to his knowledge is large that 50%. Knave - the opposite. So to the question "Will a dice show 1 or 2?" knight answers "No" and Knave "Yes".
I understand that the same effect can be achieved with usual characters and questions like "Is probability to get 1 or 2 bigger than 50%?" and I would like to see a puzzle, which can not be solved without such a probability questions.
Can you figure out a non-trivial puzzle like this?