It depends on the classifier, but yes there is a big chance that instances have same score (class probability). For example in Random Forest the class probability for each instance is calculated as number of occurrences of a particular class over number of trees, so there is going to be a lot duplicates (MAX number of unique values would be the number of trees).
Even though the calculation of class distribution varies from one classifier to another, I could guess that they are going to have repeated values.