There seems to be an important distinction between two types of probability. Let's say there's some object O with a property P1, but you don't know what other properties it has. Further suppose that what you're really interested in is whether O has some other property P2. What's the probability that O has P2? We could interpret this as an epistemic question, whereby we abstract away all the unknown details of O and just ask what proportion of P1-objects also have P2. Here we aren't really talking about the specific object O at all. We treat it merely as a token of type "P1-object", without regard for the multiplicity of other (unknown) ways O might be categorized. That's one option. Alternatively, we might focus on the concrete object O, and ask: of this specific object, including its many other properties that we are not yet aware of, how likely is O to have P2? This is a question about the real or metaphysical modal properties of O, rather than being a purely epistemic question. Let's illustrate the distinction with a couple of real-world examples.
The first example came up in the comments to my recent post on ad hominems. Suppose a notoriously unreliable person makes an argument. You are wondering whether the argument (O) is likely to be a sound one (P2), given that it is being made by this notoriously unreliable person (P1). One way to answer this would be to abstract away from the details of the argument itself, and just use your background knowledge of the advocate's unreliability - in particular, that most of his arguments are unsound - to conclude that this argument is therefore likely unsound. This is a classic ad hominem fallacy. Although such abstraction may be rational in a sense, it isn't really fair on the argument in question. After all, you've completely ignored the argument itself, when the dialectical norms of civil discourse recommend that we consider each argument on its own merits.
This latter suggestion is taken seriously by the concrete probabilist. He focuses on the argument (object O) rather than who makes it (property P1). In particular, he recognizes that the validity of the argument is metaphysically independent of the person making it. So he ignores the person, and instead assesses the argument on its own merits, trying to determine whether it is logically valid, and how plausible the premises are. It is from these considerations that he estimates the soundness of the argument.
The second example is provided by stereotyping individuals (e.g. racial profiling). Say you want to know whether Jack (O) committed the crime (P2), when the only other information you have about him is that he is a black male (P1). You can probably tell what comes next. The abstract probabilist ignores all the complexities of Jack the individual, and makes his judgment in light of how many other black males have been known to commit crimes. As with the ad hominems, we can see that this prejudice is rational in a sense, but also incredibly unfair to Jack as an individual. Your judgment of him is based on what you know of others who share the same property as him (i.e. of being a black male), rather than anything concrete and intrinsic to Jack himself. I argue elsewhere that this is morally problematic.
Consider a pair of cross-racial "twins", Alan and Bill, who are identical in all respects except that Alan is white and Bill is black. Clearly this is a difference that makes no difference. As a matter of fact, each is equally likely to make any particular decision, or have any other property or characteristic. These facts are what determine concrete probabilities, and they are unaffected by whether we know about them. But abstract probability is an epistemic notion. If all you knew was that Alan was white and Bill black, then you would judge their abstract probabilities very differently. You might think Alan is likely to be wealthier, better educated, and so forth. But these "probabilities" are metaphysically superficial -- merely reflecting facts about group frequencies and correlations. Concrete probability is much deeper, being grounded in causal and explanatory facts about the concrete individuals themselves.
So, like I said, this strikes me as an important distinction. (If someone with more formal training in statistics can go beyond the intuitive graspings I've offered here, please do leave a comment.) I think the close analogy between ad hominems and sterotyping is also interesting to note.