In this case, it does two things. One, it shows the duke as the dominant personality in the duo. Throughout their adventures, these two criminals are constantly trying to "one-up" each other. At this point, we see the masks swept aside, & we know the duke is the one in charge. Nothing the king says after this will bring back his power-he has become the subordinate one.
The second implication is that Huck and Jim are free for awhile. Neither of the criminals suspects them anymore, although the king knows he didn't move the money. It gives Huck more time to think of a plan to get rid of the two , and saves them from certain death.