What we have here is a classic Bayesian problem of parameter and process uncertainty.
Firstly there is the process uncertainty. This is the randomness associated with life itself. If both men had had at this woman endlessly for an entire month, alternating every 30 minutes or so, then there would be a 50/50 chance as to which of them had impregnated her. In other words, even if we know all the starting conditions, there is still randomness in the result.
But then there is the parameter uncertainty. We don't actually know all the starting conditions. We know nothing of relative fertility, who did who to what and when, all these kind of things. So we can't accurately estimate the process uncertainty.
I'm pretty sure that this is the thought process that the chap on Jeremy Kyle went through before he -- probably entirely accurately -- gave his 90% estimate of fatherhood.