What idea about the stolen knife does tom give to the constable and wilson

Tom takes out his frustration on Wilson and Constable Blake, who he runs into on the street. He goads the two men about their inability to apprehend the old woman that is allegedly responsible for the town robberies. Further, he plants suspicion about the twins in the two men's minds. Tom does this by first uncovering Wilson's plot to catch the thief: The five hundred dollar reward for the knife was publicly advertised, while the reward for the thief was privately communicated to the pawnbrokers. That way, the thief - unaware that there was a bounty on her head - would feel comfortable going into a pawnshop to sell her loot, and would promptly be captured. Tom points out that this scheme is foolproof, and that had the knife actually been stolen, the thief surely would have been uncovered by now. The only possible explanation, he postulates, is either that no such knife ever existed, or the twins still possess it themselves. He further notes that this would allow the twins to look wealthy and important by offering up the reward, without actually costing them anything. This explanation completely wins over the constable, and even causes Wilson to doubt the twins.