The assessment of the doubt may involve probability theory--but that isn't science, it's mathematics, which is built on logic, not on empiricism. Empiricism has so thoroughly internalized mathematics that some forget that that isn't where probability theory came from. It's not experiment which proves statistics are useful--it is statistics which prove experiments useful. Where does statistics derive its truth from? You can't use statistical modeling to explain why statistical modeling explains things!
The role of math and logic in science is not dissimilar to that of grammar in ordinary communication.
"Outside my house, elephants are flying in a sky filled with flowers" it's a perfectly valid sentence from a grammar point of view, but that by itself is not enough to say if it is also an accurate description of reality. That requires somebody going outside my house, and looking at the sky.
A more scientific example: the math of Newtonian gravity works perfectly fine with two mass signs. The conclusion that there is no negative mass is purely an empirical one.
Math and statistics can tell you how to properly combine your observations of the world to get to the least misleading conclusions, but cannot tell you the results of those observations in the first place.