It depends on what the constant is - and of course the location function is delivering 0 everywhere. A location function delivers the probability that the object is at the location referenced by the paramters fed in. The location function for a crystal ball in its excited state will deliver the value 0 for the probability that the ball is at the location for which the function is being called.

The ball is excited by being forced to provide an answer to an esoteric question like "what on earth is this idiot refusing to tell us that would enable us to help him". But when a searcher for esoteric knowledge reaches a situation where he knows exactly how fast he is solving the OP's problem(his speed is exactly zero - which in quantum mechanical terms means he's not just getting nowhere, he's already there), the probability of him being in a given location is (according to Mr Heisenberg) exactly the same as the probability of him being in any other location, and one in infinity is zero; thus he has the same location function as an excited crystal ball, so he may by chance happen to get hold of it and calm it down for long enough to ask it a question and force it to answer - of course once he's caught the ball he doesnt know how exactly fast he's going, as he doesn't know how long it will take him to get the ball calm enough to do some work and on top of that he will have to do some thinking about the actual problem, so he and the ball now have a fuzzy location rather than none at all. But being forced to answer excites the crystal ball again so as soon as the ball has identified the problem for him it is once again has zero probability of being in any particular place, so it disappears.

Well, we don't know where the dark matter is either - it's almost as bad as the crystal balls; or perhaps even worse than them, as at least the difficulty of finding crystal balls has a reasonable explanation.