Consider the help system of Example 10.5 (page 469).

(a) Using the c1 and wij counts in that example, give the probability of P(H | q), the distribution over help pages given q, the set of words in a user query.

Note that this probability needs to also depend on the words not in q.

(b) How can this be computed in time proportional to the number of words in q, rather than the size of the vocabulary. [Hint: Consider the probability of H given no words were in the query – which is not the prior of H – and then adjust for the words in the query.]