Given two different messages, A and B (maybe 20-80 characters of text, if size matters at all), what is the probability that the MD5 digest of A is the same as the MD5 digest of B and the SHA1 digest of A is the same as the SHA1 digest of B? That is:
(MD5(A) == MD5(B)) && (SHA1(A) == SHA1(B))
Assume no malicious intent, i.e., that the messages are not selected with an aim of finding a clash. I just want to know the odds of this happening naturally.
I'm thinking the chances are "astronomically low," but I'm not sure how to verify this.
More information: the size of the pool of possible messages is restricted, but large (several hundred million). Birthday paradox situations are exactly what I'm worried about.