It is possible to interpret precision and recall not as ratios but as probabilities:
* Precision is the probability that a (randomly selected) retrieved document is relevant.
* Recall is the probability that a (randomly selected) relevant document is retrieved in a search.
This page contains some illustrations to better understand the definitions of Precision and Recall:
Also, this paper relates Precision-Recall curves to the Receiver Operator Characteristic curves:
Finally, this page is further explaining the concepts and elaborating on the F-measure metric that tries to combine Precision and Recall into one measure: