 The conception of validity we have been using (PPP) takes as central the fact that premises may be accepted with degrees of confidence less than certainty. Now, anything which satisfies PPP satisfies CPP. And for argument involving only factual propositions, the converse is also true: the same class of arguments necessarily preserves truth, necessarily preserves certainty and necessarily preserves probability in the sense of PPP. But arguments involving conditionals can satisfy CPP without satisfying PPP. The invalid argument forms above do preserve certainty: if you assign probability 1 to the premises, then you are constrained to assign probability 1 to the conclusion (in all probability distributions in which the antecedent of any conditional gets non-zero probability). But they do not preserve high probability. They do not satisfy PPP. If at least one premise falls short of certainty by however small an amount, the conclusion can plummet to zero.