Prior probability for classifiers

Hello
In the fitcsvm method for training a SVM classifier one can set the prior for each class with the 'prior' flag. For most other classifiers this is also possible.
In the algorithm description I did not find any hint how this prior is incorporated in the training or the prediction. It is only described how the prior changes when e.g. a cost is incorporated etc.
How is the prior incorporated into training and prediction?

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