Can I have a multiclass classification problem with more prediction classes than real classes?

For example: I want to predict the channel the user is going to watch. The real classes are "user didn't see tv" and "user saw channel C". The prediction classes are "user will not watch tv", "user will watch channel C", "user will watch one of two channels: C or D".

Is this a good formulation of a classification problem?

How can I calculate the performance metrics as recall, precision, and F1-score per class?



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