Assuming randomness (what does that really mean in this context?), each bit has a 50% chance of flipping the way it did. So the the probability of each hypothesis is $(\frac{1}{2})^n$ where $n$ is the number of bits in the hypothesis. This means longer hypotheses are less likely, i.e. they require additional evidence compared to the shorter hypotheses. (these probabilities are not normalized, but still comparable)