Probabilistic determination of syzygy

Is there a framework for describing the probabilistic confidence of an $N$-body syzygy? Forgive me if I’m misusing terminology: I’d like to know how physicists/astronmers model the confidence of "alignment" of celestial bodies on one axis. It is not quite superposition in quantum mechanics where (let’s say) 2 objects completely co-habitate the same space.

Not sure if Astronomy or Physics is the best place for this discussion. I have an analogous problem wherein I have $N$ observations in 3D space, each observation has a Gaussian-like point-spread function and the theoretical (but not observed) physical distance separating each observation is known beforehand. I’d like to determine a probabilistic confidence of the alignment of the N objects in 3D space.