A simple informal reason for giving a small probability to "A causes B" could be this:

For any fixed values A and B, there is only one explanation "A causes B", one explanation "B causes A", and many explanations "C causes A and B" (for many different values of C). If we split 100% between all these explanations, the last group gets most of the probability mass.

And as you said, the more complex given field is, the more realistic values of C there are.