No, the uncertainty principle is a statement about the behavior of non-commuting operators in a Hilbert space. It is not a probabilistic statement. It doesn't even have anything to do with probability until you apply it to a probabilistic interpretation of quantum mechanics, where vectors in the Hilbert space have something to do with probability. The understanding you are referring to is more or less correct, but is a specific application to certain interpretations of quantum mechanics. It's also useful to think about it this way experimentally (in terms of "uncertainty"), which is why most people learn it this way in early physics classes and where the name comes form.

Perhaps I have made the same mistake as you, and was thinking about the practical but non-generalized way the second law of thermodynamics is usually taught, which includes concepts like "the system will be in this state". The only part of your statement that is still probabilistic is "entropy will not decrease". That's not really true; it probably won't decrease.

>neither of which gives a prediction

"entropy will not decrease" is a prediction. It is possible (albeit overwhelmingly unlikely over large time scales) that this prediction is sometimes false.