A&B gains more evidence than A from the experiment. It doesn't (and can't) become more probable.

Let's have an example. Someone is flipping a coin repeatedly. The coin is either a fair one or a weighted one that comes up heads 3x as often as tails. (A = "coin is weighted in this way".) The person doing the flipping might be honest, or might be reporting half the tails she flips (i.e., each one randomly with p=1/2) as heads. (B = "person is cheating in this way".)

Let's say that ahead of time you think A and B independently have probability 1/10.

Your experiment consists of getting the (alleged) results of a single coin flip, which you're told was heads.

So. Beforehand the probability of A was 1/10 and that of B was 1/100.

The probability of your observed results is: 1/2 under (not-A,not-B); 3/4 under (not-A,B); 3/4 under (A.not-B); and 7/8 under (A,B).

So the posterior probabilities for the four possibilities are proportional to (81:9:9:1) times (4:6:6:7); that is, to (324:54:54:7). Which means the probability of A has gone up from 10% to about 14%, and the probability of A&B from 1% to about 1.6%.

So you've got more evidence for A&B than for A, which translates (more or less) to a larger relative gain in probability for A&B than for A. But A&B is still less likely.

If you repeat the experiment and keep getting heads, then A&B will always improve more than A alone. But the way this works is that after a long time almost all the probability of A comes from the case where A&B, so that A&B's advantage in increase-in-probability gradually goes away.