Coincidences

I've been thinking about how coincidences are evaluated in forensics.  How does one separate the pure coincidences from the can't-be-coincidences?

Supposedly, a detective does not believe in coincidence.

Let's say George has some mysterious charges on his bill.   Let's say that something comes to light that the exact digits of his credit card number appeared in a text from a Hans whom George doesn't know, but say George's daughter knows Hans.  There might be enough digits in that number to warrant thinking that it is not a coincidence -- that is, that those doesn't represent something else: a book-of-the-month club user registration, a hotel confirmation number, etc.  A long enough number is supposed to use up probabilitic resources.  After all, it should be the case that a random sequence of digits probably NOT be valid credit card number.  There could be a preponderance of evidence that Hans

To make this more interesting, let's say that these mysterious charges occurred shortly after George died under mysterious circumstances and his credit card went missing.  There is the proximity to George: two degrees of separation.  There is the time proximity: near the time of George's death.

To a detective, this forms a pattern, a specification.  Now the small probability is much larger than the Universal Plausibility Bound, but it is still compelling in many cases, once motive and alibi are dealt with.

The quality Dembski would call tractability, gets into the degrees of separation along with the specificational resources.  What are the chances that someone would have the credit card number and also that this person be only two degrees of separation from the credit card owner, close to the time the card went missing?   Too coincidental?   How to put some firm numbers behind that assessment?  I suspect that departments of justice deal with tractability all the time, and somehow it is not pseudoscience  despite the problem resisting really precise calculations in a lot of cases.