This work addresses an anomaly involving probability and logic relative to the interpretation of implicative statements, and the evaluation of those statements compatible with conditional probability. One of our chief motivations is the need to formalize rigorously the connections between conditional probability and the hidden logic of implicative statements, such as production rules in expert systems and defaults in common-sense reasoning. The purpose is to provide theoretical results for probabilistic reasoning that will be useful in the design and evaluation of inference rules of such systems.