I am trying to understand the probability calculations using Bayes theorem for a ham/spam classification problem (that uses Naive Bayes). I have a training set of ham and spam data with appropriate labels and assume that ham or spam can occur with the same probability.
So for a given text $(T)$ to classify as ham/spam I am using the following equation:
$P(Spam|T) = \frac{P(T|Spam)}{ P(T|Spam) + P(T|Ham)}$
I don't multiply the terms in the numerator with $P(Spam)$ or $P(Ham)$ since they are equal and would cancel out each other. Is this a correct model? The $P(T|Spam)$ just uses a naive multiplication of probabilities of individual words precalculated based on training data.