It's actually much simpler - on the surface - than what that quoted item implies!
Probability learning is literally "learning" what the "probability" is of certain things, the study of how people and other animals learn about real world probabilities outside a statistics classroom, and in cognitive science (like in the PDF you linked) the concern is about strategies, methods, and the real world mechanics of how intelligent creatures actually manage to figure this stuff out; of course, sometimes the answer is just "wow, people are really bad at this!"
When your quoted text says that "probability of a response tends to match the probability of the reinforcement", this is not a maxim to live by - it does not describe, necessarily, how you should behave. Put in jargon, it's descriptive, not prescriptive. It's not a question of rationality at all.
What it does correctly describe is that many animals are pretty good at modifying their behavior to match the unpredictable nature of our world. In the real world, this means things like:
- what route to take to work to avoid delays or accidents
- how to dress for the weather (hot/cold, rain/snow, etc)
- gambling games of all kinds ("come on Box Cars!")
- where to eat to avoid food poisoning
In animal research, that paper by Aczel mentions experiments where rats have a T-maze, where they look for food to the left or to the right. Originally behaviorists were just interested in learning and unlearning of things like "the cheese is always on the left side", and they found that rats figured this out and would (sensibly) usually go to the left side first in expectation of the food.
Then some smarty-pantses wondered what would happen if there was only a certain probability of food being in a certain place, and how this might effect the rat behavior. It turns out that they end up figuring out what the best place to go is and altering their behavior according to how lopsided the observed probability seems (so if it's 60:40 they might hardly prefer one side to the other at all, but with 75:25 they don't exclusively search the one side that is more likely - they just prefer it according to the probability). This means that the probability of the response (choosing the left side) tended to match the probability of the reinforcement (getting food). Makes sense, right?
This also explains why most people aren't compelled to run along every vending machine they see to search for forgotten change; sure, sometimes you do get change this way, but you usually don't, and from this we can reasonably predict that most people won't engage in this sort of change-tray-obsessed behavior. Obviously this system is open to peculiarity, like the lottery or insistence on behavior that no past experience indicates will work.
And this leaves us to cognitive research, where enterprising folks try to figure out the HOW of dealing with the probabilistic nature of life, where you never know what you are going to get - yet we do seem to get a 'feel' for how likely something is without having a statistician run 10000 trials and give us an analysis a year later. How do we do that, anyway? I dunno - I haven't read enough probability learning research!
As to how to use this in your everyday life, it would I suppose be about how to get better at doing it yourself by avoiding poor strategies (though you'd probably be better learning more about statistics directly), or about teaching others to get better at the same. I don't know if learning about the 'how' of probability learning is as useful as the 'how' of memory, but this is pretty well outside my field of interest so I can't say.