I think you have this oversimplified. Stringing together inferences can take us in either direction. It really depends on how things are being done and this isn't always so obvious or simple. But just to show both directions I'll give two simple examples (real world holds many more complexities)

It is all about what is being modeled and how the inferences string together. If these are being multiplied, then yes, this is going to decreases as xy < x and xy < y for every x,y < 1.

But a good counter example is the classic Bayesian Inference example[0]. Suppose you have a test that detects vampirism with 95% accuracy (Pr(+|vampire) = 0.95) and has a false positive rate of 1% (Pr(+|mortal) = 0.01). But vampirism is rare, affecting only 0.1% of the population. This ends up meaning a positive test only gives us a 8.7% likelihood of a subject being a vampire (Pr(vampire|+). The solution here is that we repeat the testing. On our second test Pr(vampire) changes from 0.001 to 0.087 and Pr(vampire|+) goes to 89% and a third getting us to about 99%.

[0] Our equation is

                  Pr(+|vampire)Pr(vampire)
  Pr(vampire|+) = ------------------------
                           Pr(+)

And the crux is Pr(+) = Pr(+|vampire)Pr(vampire) + Pr(+|mortal)(1-Pr(vampire))