What are the typical values of probabilities for nonspecific binding to an antibody?
TL;DR Specificity of antibody can be not superb. It can give false-positive results in up to 90% of experiments. However, some essay are 90% specific.
That is an interesting question and there sure a lot of research done to understand specificity and strength of binding of antibody to its target.
First of all, let me say that antibody-epitope interaction is, as many biological processes, probabilistic process, which means it can go either way, however, after binding antibody need a lot more energy or time to &quot;fall off&quot;. Direct contact is always required for establishment of non-covalent bond between antibody and epitope, because characteristic length of that interaction is very low (order or angstroms, 0.1nm and less). Point here is that you don't need to run antibody in stream, rather let is sit in solution with your sample or mix gently, random thermal motion will take care of them finding each other. In flow you will waste a lot of antibody, which is expensive.
I think that you can estimate probability of given antibody binding given molecule from their 3D structures, but this is extremely burdensome calculation. What you can do experimentally, I suppose, is label &quot;right&quot; epitope with red fluorescent tag, and every other molecule in your solution with green tag. Then run solution through column with antibody sitting on beads (as in chromatography), elute everything and compare green to red signal. Measuring accurately, this will tell you how much &quot;junk&quot; antibody picked out of solution.
Now, to numbers. Here Abcam talks about its antibody for progesterone. Molecules, closely related to progesterone, are recognized with 40-90% efficiency, compared to true-positive target (progesterone). But this is absolute-worst case scenario, because those molecules are so closely related.
On other note, antibody specificity is very important when essay is used, e.g. for HIV diagnosis. Here is nice page from U Penn, that discusses issues with specificity:

For example, in one study of 290,000 asymptomatic Minnesota blood donors donating 630,000 blood units, the false positive rate when both the screening and confirmatory assays were positive was was 0% per donation (95% confidence interval 0% to 0.0006%).
...
For example, in one study of asymptomatic Italian blood donors, only about 13% of donors with repeatedly-reactive EIA tests were confirmed to be HIV-infected on the basis of positive immunoblot. However, in a high risk population the false-positive rate can be much lower, as low as 1-3%.

I couldn't find any more precise data or studies. In biological imaging (my field) antibodies are split into &quot;works&quot; and &quot;don't work, drop it&quot; (aka high background) groups.