I'm not sure how much this will help you but I hope it gives some pointers.
Here is a Mathematica function which computes the probability under the distributions for a circle of radius separation/2 for two ships with a normal distribution of position with variance 0.2. A variance of 0.2 is close to the 95% certainly level.
In brief it defines a mixture distribution in 2 dimensions with covariance matrix {{0.2,0},{0,0.2}} (* other covariance matrices would account for elliptical distributions *). Forms the probability distribution function for that mixture and then numerically integrates it over the required range.
(* Uses absolute separation distance rotated to the x axis *)
probProximity[reportedSeparationMiles_, probabiityRangeMiles_] :=
With[{dist = MixtureDistribution[{1, 1},
{MultinormalDistribution[{-(reportedSeparationMiles/2),0}, {{0.2, 0}, {0,0.2}}],
MultinormalDistribution[{ reportedSeparationMiles/2, 0}, {{0.2, 0}, {0,0.2}}]}]},
NIntegrate[
PDF[dist][{x, y}]
Boole[Abs[\[Sqrt]((0 - x)^2 + (0 - y)^2)] <= probabiityRangeMiles/2],
{x, -(probabiityRangeMiles/2), probabiityRangeMiles/2},
{y, -(probabiityRangeMiles/2), probabiityRangeMiles/2}]]
The probability distribution of position for two ships 5 miles apart with a 95% confidence of being within one mile of reported position.
For a range of 5 miles, the calculated value is
probProximity[5, 5]
0.464173
Here is the probability of proximity over a range of distances:
