How does Facebook Sharer select Images and other metadata when sharing my URL?

Question

When using Facebook Sharer, Facebook will offer the user the option of using 1 of a few images pulled from the source as a preview for their link. How are these images selec

Answer 1

Old way, no longer works:

Reported new way, also does not work:

It randomly worked off and on during the first day I implemented it, hasn't worked at all since.

The Facebook linter page, a utility that inspects your page, reports that everything is correct and does display the thumbnail I selected... just that the share.php page itself doesn't seem to be functioning. Has to be a bug over at Facebook, one they apparently don't care to fix as every bug report regarding this issue I've seen in their system all say resolved or fixed.