Recent studies have shown the existence of two qualitatively distinct groups of people based on how they judge the probability of a conditional statement. The present study was designed to test whether these differences are rooted in distinctive means of processing conditional statements and whether they are linked to differences in general intelligence. In the study, each of 120 participants completed three separate cognitive tasks involving the processing of abstract conditional statements--the probability-of-conditionals task, the conditional truth table task, and the conditional inference task--in addition to completing a test of general intelligence (AH4). The results showed a number of predicted effects: People responding with conditional (rather than conjunctive) probabilities on the first task were higher in cognitive ability, showed reasoning patterns more consistent with a suppositional treatment of the conditional, and showed a strongly "defective" truth table pattern. The results include several novel findings and post challenges to contemporary psychological theories of conditionals.