The whole point of probabilistic modeling is to replace absolute decisions like "right or wrong" by continuous weights on the possibilities. If you absolutely need a definite decision, you can sample a prediction according to the probability assigned by the model. If the true outcome is x and the model assigned it probability p, then that procedure is going to be wrong (1-p) of the time. You could define that number as the "wrongness" of the probabilistic model, as a continuous analog of the definite case.
The advantage of probabilistic modeling is that you can also ask how wrong the model expects to be and get a meaningful answer. If there are many possible outcomes and none of them very likely, any choice is going to be wrong a lot. But you should expect a good model to have a small difference between its expected and actual wrongness. One might call that value "honesty".