Noisy measurement in 2D space

Hi,

I've got a solution to a problem I'm having that I'd love some confirmation for.

Say, you've got a noisy measurement in 2D space. You know that the distance between the true origin and the measurement is governed by a normal distribution with a standard deviation of s.

Can I then say that the probability for some point p' being the real origin of a measurement p is proportional to N(d,s)/d if d is the distance between p and p'?

My reasoning is that the number of points at distance d from p is proportional to d and thus, for every point p' at distance d, the probability of it being measured instead of p is the probability of the measurement being off by d times the probability of it being the one out of all points at that distance.

The thing is, I'm actually pretty convinced this is correct, but my algorithm doesn't work and I'd like to know for sure this is not the part where I'm making a mistake.

Thanks, cheers,

Johannes