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>In the situation where knowledge of guilt has been found by unjust means, how does ignoring that knowledge promote justice.

By signalling to police that whatever sketchy things they did to obtain the knowledge won't be available to help them achieve their goal.

Example, police use defective probable cause to search a motorist's vehicle; and I don't just mean search, but really search, as in pull the carpets up, remove interior panels, remove all of the contents of the trunk, break down the tires and look inside; it is destructive. Although the car may be re-assembled, they never are returned to their pre-tossing state. The only thing preventing this from happening more often is the amount of labor involved in tearing the car up. Police (Feds sometimes do) don't have to pay for damaging someone's property when they do this. They don't even have to put it back together. Same goes for your home.