Could someone point to results or proofs about the probability of $$HMAC(k, m_1) = HMAC (k, m_2)$$ assuming the underlying hash function is SHA-256? Would those probabilities be higher/lower if $m_1$ and $m_2$ are not independent?
Please don't point to birthday attack results. I am only interested in the probability that the tags are equal given two messages (random or not) and a single key.