It's just the usual explanatory/contextual の combined with the -ば form.
It's different in the same way 叶わないのだ/です is different from 叶わない/叶いません in that it's framed as referring to some context rather than just a statement made in a vacuum.
The English parallel isn't perfect, but it's similar to the difference between "If (the situation) won't be realized" and "If it's the case that (the situation) won't be realized", i.e. the latter more strongly suggests that the speaker has realized or resigned himself to the fact that the situation in question is indeed what has happened (or is going to happen).
(Incidentally, 叶わない(の)なら, which you asked about previously, would have a similar nuance.)