Identifying driver mutations in cancer is notoriously difficult. To date, recurrence of a mutation in patients remains one of the most reliable markers of mutation driver status. However, some mutations are more likely to occur than others due to differences in background mutation rates arising from various forms of infidelity of DNA replication and repair machinery, endogenous, and exogenous mutagens. We calculated nucleotide and codon mutability to study the contribution of background processes in shaping the observed mutational spectrum in cancer. We developed and tested probabilistic pan-cancer and cancer-specific models that adjust the number of mutation recurrences in patients by background mutability in order to find mutations which may be under selection in cancer. We showed that mutations with higher mutability values had higher observed recurrence frequency, especially in tumor suppressor genes. This trend was prominent for nonsense and silent mutations or mutations with neutral functional impact. In oncogenes, however, highly recurring mutations were characterized by relatively low mutability, resulting in an inversed U-shaped trend. Mutations not yet observed in any tumor had relatively low mutability values, indicating that background mutability might limit mutation occurrence. We compiled a dataset of missense mutations from 58 genes with experimentally validated functional and transforming impacts from various studies. We found that mutability of driver mutations was lower than that of passengers and consequently adjusting mutation recurrence frequency by mutability significantly improved ranking of mutations and driver mutation prediction. Even though no training on existing data was involved, our approach performed similarly or better to the state-of-the-art methods.