Developments in machine learning together with the increasing usage of sensor data challenge the reliance on deterministic logs, requiring new process mining solutions for uncertain, and in particular stochastically known, logs. In this work we formulate trace recovery, the task of generating a deterministic log from stochastically known logs that is as faithful to reality as possible. An effective trace recovery algorithm would be a powerful aid for maintaining credible process mining tools for uncertain settings. We propose an algorithmic framework for this task that recovers the best alignment between a stochastically known log and a process model, with three innovative features. Our algorithm, SKT R, 1) handles both Markovian and non-Markovian processes; 2) offers a quality-based balance between a process model and a log, depending on the available process information, sensor quality, and machine learning predictiveness power; and 3) offers a novel use of a synchronous product multigraph to create the log. An empirical analysis using five publicly available datasets, three of which use predictive models over standard video capturing benchmarks, shows an average relative accuracy improvement of more than 10% over a common baseline.