Binary star system - Revolution around Primary vs Companion How likely is it in a binary or multi-star system for a non-star celestial body to revolve around the primary star rather than the companion star?
 A: This is not my field, but the question is interesting so I'll give you my best answer.
The sphere of influence of an isolated astronomical body (in this case the binary stars, treated as a unit) is not well-defined; therefore, some of the forthcoming argument requires more information about the context in which you are studying the binary system (like the mass and relative location of the galactic center blackhole).
As a first-order approximation, let's assume that the orbiting matter will be co-planar with the stars, then matter orbiting the primary star will lie within its Roche Lobe (and likewise for the companion). All other material (even that which lies within the radius from the center of mass to $L_2$) will be considered to be circumbinary.
Therefore, assuming a uniform probability distribution, the likelihood of a particular object orbiting the primary star is given by
$$
P=\frac{A_1}{A_{SoI}}
$$
And the relative probability that it will orbit the primary star as opposed to the companion is
$$
P'=\frac{A_1}{A_1+A_2}
$$
where $A_1, A_2, \text{and}\ A_{SoI}$ are the planar areas of the primary star's Roche lobe, the companion star's Roche lobe, and the system's sphere of influence, respectively. However, as previously noted, calculating these areas requires more information about the system (mass ratio, eccentricity, separation distance, etc.).
Of course, this is all quite simplified and could probably be improved by determining the actual probability distribution of circumstellar matter and taking into account out-of-plane bound orbits. That being said, the actual probability distribution would be difficult to calculate since I am not aware of a well-established model for planetary mass distribution (relevant: Frost Line). Additionally, most significantly out-of-plane orbits near the stars would be highly unstable, so that adjustment might not have much of an effect.
Another way of answering this question would be to address how often we actually observe S-type orbits (around one star) versus P-type orbits (around both stars) in binary systems. 
According to the following articles, it appears that circumbinary planets have certainly been observed, but as far as I can tell, there doesn't appear to be particularly strong observational evidence to determine if any of these exoplanets are either circumprimary or circumsecondary. However, some numerical models do bear out the possibility of S-type orbits by establishing their stability.
Existence:
http://arxiv.org/abs/1210.3055
http://arxiv.org/abs/1210.3612
http://arxiv.org/abs/1010.4048
http://www.mpia.de/homes/henning/Publications/daemgen.pdf
Stability:
http://adsabs.harvard.edu/full/2002ESASP.518..547P
http://montgomerycollege.edu/Departments/planet/planet/Planetary%20Definition/doubleStars.pdf
