Actually, you problem is a permutation problem.
but we can solve it using the result we already got.
let P3 denotes the probability of have 3 successive
successes in the 10 trials. P4 denotes the probabilty
of having 4 successive successes.
the answer of your problem is: P3-P4.
let P3n denotes the probability of the fist apperance of
3 successive successes in n trials. which is already sloved
by you,then we can get P3 easily.
P3 = P33+P34+P35+...P310.
we can work out the P4 in the same way.