Most developed implementation is BayesDB[1], but there's a lot of ideas coming out of a number of places right now.
e.g. store customer orders in the DB, and query `P(c buys x | c bought y)` in order to make recommendations - where `c buys x` is unknown, but `c bought y` occurred, and we know about 'other cs' x and y.
Is that sort of how it works?
The way I see, the real utility comes from the fact that domain models such as those in a company's data warehouse are typically very complex, and a great deal of care often goes into mapping out that complexity via relational modelling. It's not just that c bought x and y, but also that c has an age, and a gender, and last bought z 50 days ago, and lives in Denver, and so on.
Having easy access to the probability distributions associated with those relational models gives you a lot of leverage to solve real life problems with.
http://empirical.com (still dark atm)
co-founded by CEO Richard Tibbetts, who was also a co-founder of StreamBase (acquired by TIBCO).
I'm curious to know if it's related to the current discussion.