Association rules provide a concise statement of potentially useful information, and have been widely used in real applications. However, the usefulness of association rules highly depends on the interestingness measure which is used to select interesting rules from millions of candidates. In this study, a probability analysis of association rules is conducted, and a discrete kernel density estimation based interestingness measure is proposed accordingly. The new proposed interestingness measure makes the most of the information contained in the data set and obtains much lower falsely discovery rate than the existing interestingness measures. Experimental results show the effectiveness of the proposed interestingness measure.