Branch length (BL) and posterior probabilities (PPs) are not correlated variables between themselves, or even with regard to maximum likelihood (ML). You can think of the first two as "local" variables that describe distances between tree members (BLs) or how likely a particular branch topology is (PPs). Following that analogy, ML is a "global" variable that describes the relative fitness of the whole tree topology.
What this means is that we can have identical BLs but different PPs of the same branch in two different contexts. It also means that if you add a new member to a tree, the ML with change (it will decrease) even if the overall topology, individual BLs and PPs remain the same. In a nutshell, ML is negatively correlated with the alignments size (# columns * # members). BLs are positively correlated with member distances. PP estimates how likely a given topology is, which in general is not correlated with either BLs or ML.