 For example, in the case of Pearl’s sprinkler, since rain is causally prior to the sidewalk’s being wet, the causal structure of the situation does not ensure that the rain is probabilistically independent of whether the sprinkler is on, given the fact that the sidewalk is wet. That is, we have no grounds for thinking that the probability of rain, conditional on the sidewalk’s being wet, is identical to the probability of rain, conditional on the sidewalk’s being wet and the sprinkler’s being on (presumably, the former is higher than the latter). This failure of independence prevents us from using the (Wet \(\Rightarrow\) Rain) default, in the presence of the additional fact that the sprinkler is on. 