Measurement-based probabilistic timing analysis (MBPTA) computes trustworthy upper bounds to the execution time of software programs. MBPTA has the connotation, typical of measurement-based techniques, that the bounds computed with it only relate to what is observed in actual program traversals, which may not include the effective worst-case phenomena. To overcome this limitation, we propose Extended Path Coverage (EPC), a novel technique that allows extending the representativeness of the bounds computed by MBPTA. We make the observation data probabilistically path-independent by modifying the probability distribution of the observed timing behaviour so as to negatively compensate for any benefits that a basic block may draw from a path leading to it. This enables the derivation of trustworthy upper bounds to the probabilistic execution time of all paths in the program, even when the user-provided input vectors do not exercise the worst-case path. Our results confirm that using MBPTA with EPC produces fully trustworthy upper bounds with competitively small overestimation in comparison to state-of-the-art MBPTA techniques.