It has recently been argued that a non-Bayesian probabilistic version of inference to the best explanation (IBE*) has a number of advantages over Bayesian conditionalization (Douven [2013]; Douven and Wenmackers [2017]). We investigate how IBE* could be generalized to uncertain evidential situations and formulate a novel updating rule IBE**. We then inspect how it performs in comparison to its Bayesian counterpart, Jeffrey conditionalization (JC), in a number of simulations where two agents, each updating by IBE** and JC, respectively, try to detect the bias of a coin while they are only partially certain what side the coin landed on. We show that IBE** more often prescribes high probability to the actual bias than JC. We also show that this happens considerably faster, that IBE** passes higher thresholds for high probability, and that it in general leads to more accurate probability distributions than JC.