At the beginning of the story, all present save Morris believe the story about the paw to be simply a fairy tale. They do not truly think that the paw can cause magic; Mrs. White sums it up with her comment:
"The idea of our listening to such nonsense! How could wishes be granted in these days?"
After Herbert's death, both are stricken with depression; it is possible that it was simple coincidence, that Herbert would have been killed regardless of their wish, but it seems too perfectly suited to be real coincidence. Mrs. White is the first to fully acknowledge the paw's power and hopes to reverse their luck by using it again.
"We've only had one."
"Was not that enough?" he demanded fiercely.
"No," she cried, triumphantly; "we'll have one more. Go down and get it quickly, and wish our boy alive again."
Mr. White calls this idea "foolish and wicked," but makes the wish to assuage his wife, who is on the verge of a depressive breakdown. His full belief is not solidified until he realizes what he has done, and that the knocking is not from a living, ordinary Herbert, but of a thing that was never meant to exist. In that moment, he believes fully, and:
...grop[es] wildly on the floor in search of the paw. If he could only find it before the thing outside got in.
(Jacobs, "The Monkey's Paw," gaslight.mtroyal.ca)
They are convinced by the turn of events that cannot be coincidence; there is no possibility that first the money, then the knocking from a creature that vanishes, can be anything but supernatural. They therefore go from believing themselves in control of their own destiny to believing in determinism; they cannot change their fates, no matter what, and attempts to the contrary have negative consequences.