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I understand that the likelihood is calculated/estimated by looking at the number of instances where a certain feature and class occur together divided by the total instances of that class. However, I do not understand the denominator of the following function:

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Can anyone explain what the denominator does here (possibly with a numerical example)?

I think this is also the key for me to understand the following equation (again the denominator) for smoothing:

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Thank you in advance!

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