Schupbach and Sprenger (2011) introduce a novel probabilistic approach to measuring the explanatory power that a given explanans exerts over a corresponding explanandum. Though we are sympathetic to their general approach, we argue that it does not (without revision) adequately capture the way in which the causal explanatory power that c exerts on e varies with background knowledge. We then amend their approach so that it does capture this variance. Though our account of explanatory power is less ambitious than Schupbach and Sprenger's in the sense that it is limited to causal explanatory power, it is also more ambitious because we do not limit its domain to cases where c genuinely explains e. Instead, we claim that c causally explains e if and only if our account says that c explains e with some positive amount of causal explanatory power.