Say you have a binary (0 or 1 characters) string of N characters. Each character is equally likely to appear. What is the probability that there will be a substring of K 1 characters?

For instance if K = 2, N = 3 the answer is 3/8 = 37.5%. 000: NO 001: NO 010: NO 011: YES 100: NO 101: NO 110: YES 111: YES

How to solve this problem. Can it be done in polynomial time?