how to convert distance to probability

[poovich]

If I want to convert distance values to probability, are there any methods ?

[ohammer]

You can not convert one single distance value to one single p value. If you want to see if distances within two or more groups of items are significantly smaller than distances across, you can use PerMANOVA (also known as Adonis or NPMANOVA), or ANOSIM. If you want to see if one set of distances correlates with another set, you can use the Mantel test.

[SlideRule]

Although the following MIT OpenCourseWare video lecture is on numerical integration, it starts with an example of probability related to distance that I find delightful:

http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/video-lectures/lecture-24-numerical-integration/