A “well-defined” probability question is simply one in which there is a single correct answer determined by the given premises of the problem together with the axioms of a probability space. You can of course give estimates to answer probability questions that are not well-defined, and sometimes you may have to. The difference is that you can’t claim that these answers are correct and you should have much lower credence in them.
Note in particular the distinction between credence and probability! Credence may be treated as an application of probability in that you can model credences as obeying the axioms of a probability space, but not all probabilities are credences.
A “well-defined” probability question is simply one in which there is a single correct answer determined by the given premises of the problem together with the axioms of a probability space. You can of course give estimates to answer probability questions that are not well-defined, and sometimes you may have to. The difference is that you can’t claim that these answers are correct and you should have much lower credence in them.
Note in particular the distinction between credence and probability! Credence may be treated as an application of probability in that you can model credences as obeying the axioms of a probability space, but not all probabilities are credences.