Probabilistic logic languages, such as ProbLog and CP-logic, are probabilistic generalizations of logic programming that allow one to model probability distributions over complex, structured domains. Their key probabilistic constructs are probabilistic facts and annotated disjunctions to represent binary and mutli-valued random variables, respectively. ProbLog allows the use of annotated disjunctions by translating them into probabilistic facts and rules. This encoding is tailored towards the task of computing the marginal probability of a query given evidence (MARG), but is not correct for the task of finding the most probable explanation (MPE) with important applications e.g., diagnostics and scheduling. In this work, we propose a new encoding of annotated disjunctions which allows correct MARG and MPE. We explore from both theoretical and experimental perspective the trade-off between the encoding suitable only for MARG inference and the newly proposed (general) approach.