Pollock's concepts of reasons and defeaters have been widely adopted, but his anti-probabilistic treatment of argument strength less so. After an explanation of how Pollock's concerns can be addressed probabilistically, the paper continues with a formal treatment of reasons, defeaters, and argument strength, while remaining within standard probability theory and its underlying classical logic. Pollock studied puzzles about self-defeat and collective defeat (associated with the lottery paradox), and it is shown how these can be addressed probabilistically. A normative framework for arguments and their strength, as provided here, is needed for the development of rationality support tools for the prevention of reasoning errors.