In a music recognition task, the classification of a new melody is often achieved by looking for the closest piece in a set of already known prototypes. The definition of a relevant similarity measure becomes then a crucial point. So far, the edit distance approach with a-priori fixed operation costs has been one of the most used to accomplish the task. In this paper, the application of a probabilistic learning model to both string and tree edit distances is proposed and is compared to a genetic algorithm cost fitting approach. The results show that both learning models outperform fixed-costs systems, and that the probabilistic approach is able to describe consistently the underlying melodic similarity model.