They ascribe the fulfilment of their aim to a specific supplication made in a place to which the Sacred Law grants no special rank; and because supplication as such can indeed be efficacious, the mind can accept attributing the result to it—unlike the genus of vows, which has no causal power at all.
The point is this: once Satan succeeds in beautifying for them the attribution of effect to something that possesses neither intrinsic influence nor a sanctioned description, it is even easier for him to adorn the attribution of effect to a description whose genus is acknowledged to have influence. Yet just as their first belief is unsound, so too is this one, for both run contrary to the Sacred Law.
Consider the matter more closely. Anyone who imagines that a particular supplication or vow was the cause—or even part of the cause—of obtaining what he sought must offer proof. In most cases he can point to nothing but occasional coincidence: the two events simply occur together, even if one follows the other in place or time, while the instances in which they do not coincide (1)(2) outnumber the coincidental ones many times over. The mere conjunction of two things at certain times, along with myriad cases in which they fail to coincide, is by the unanimous agreement of rational people no proof of predominance (3), especially when another adequate cause exists; for the repeated absence of the effect shows that predominance is lacking (4).
Should someone say, “The failure resulted from a missing condition or the presence of an impediment,” we reply, “Rather, the coincidence was due to another cause altogether—and that is the stronger view. Indeed, at every moment we witness Allah meeting needs and relieving distress by countless means that no one could possibly enumerate.”