What does a predicted probability really mean, without considering the accuracy of the underlying model?
Accuracy is measured in classification model by comparing the predicted labels to the actual known labels.
The predicted labels are a function of both the predicted probabilities for each class and a predefined threshold(binary classification usually is 0.5)
So if sample A got predict_proba of {0: 0.2, 1: 0.8} it will be labeled as 1(since 0.8 > 0.5).
Accuracy is measure of classification correctness and predict_proba is a direct result of the model underlining function.