I understand the question but I am not sure how to solve it. For example, if we flip HHHTTTTT then the next three must be heads because of the question. This however seems counterintuitive. I believe that there are $2^{10}$ possible strings, but I am unsure of how to count all possible strings that begin with HHH. It is: When given the counts of heads and tails resulting from the flips, what is the probability that the order of the results has heads in the first three places?
