Estimating the probability of all words

Thank you for the great explanation!
To estimate the P(dear,deadline,student), we sum up the answers we got from estimating the conditional probabilities of the two classes (Ham and Spam). Why did we do that ? Why not estimating using the counts of the words dividing by the whole numbers of words ? It will not give the same answers for both cases (Ham and Spam) but still I didn't get the concept of estimating P(dear,deadline,student) using the method in the slide.