(a) All attachment sites (red, blue, and black dots) as well as the probe llocation (green dot) are known exactly in respect to the macromolecule (white surface representation). (b) All distances are known exactly. (c) Convolution of the circles with the respective location delta functions shifts the circles to be centered at their respective attachment site location. Because the probability is zero for all locations off the circles, only the intersection of all three circles has non-zero probability when the circle probability functions are multiplied. (d) The final combined probe location probability function is a delta function at the known probe location. (e) If one of the contributing parameters is incorrect, the final combined probe location probability function is zero everywhere because the circles do not intersect. (f) If uncertainties are incorporated into the probability functions, overlap of non-zero probabilities is observed. (g) The final combined probe probability function encases the correct location of the probe.