What is the likelihood of pair production for a high energy photon? Wikipedia says that pair production is the dominant form of light-matter interaction for photons with a mass equivalence of at least twice the rest mass of the target particle, implying that not all photons result in pair production. What is meant by dominant and how does dominance increases with photon energy?
 A: 
...implying that not all photons result in pair production. 

This is correct. Obviously, pair production in the form 
$$\gamma \rightarrow e^+ + e^-$$
cannot occur if the incident photon ($\gamma$) does not have an energy of at least $2m_e\approx1$MeV. (Pair production can also create other particles, not just electrons/positrons, given sufficient energy as long as all relevant conservation laws are followed.)

What is meant by dominant and how does dominance increases with photon energy?

Now for a more general answer. Photons interact with matter in several different mechanisms depending on their energy. The three "main" mechanisms are, in order of increasing energy, photoelectric absorption, Compton scattering (or the analogous Thomson scattering at low energies), and pair production. A very brief overview of these is:


*

*Photoelectric absorption is where a photon is absorbed by an atom or nucleus - think spectral lines in reverse. In order to conserve energy and momentum, this cannot occur with "point particles" such as electrons, as they have no internal degrees of freedom to simultaneously conserve momentum and energy from the collision. For high enough energies, photoelectric absorption can eject electrons from an atom (ionization). The cross section for this mechanism scales with: $$\sigma\propto \frac{Z^5}{k_0^{7/2}},$$ where $Z$ is nuclear charge and $k_0$ is photon wavenumber, which is proportional to its energy.

*Compton scattering is simply inelastic scattering of a photon from any charged particle (doesn't have to be a composite particle, unlike photoelectric absorption). Think ping pong ball "scattering" off a bowling ball. The cross ection for this mechanism is a bit more complex and given by the Klein-Nishina formula, but a simplified version of this comes from integrating the differential cross section: $$\sigma\propto\int_\Omega \left(\frac{k}{k_0}\right)^2\left(\frac{k}{k_0}+\frac{k_0}{k}-\sin^2\theta\right)dS,$$ where $k_0$ and $k$ are incident and scattered wavenumbers, respectively. You don't really need to know what this means to understand it - the important aspect is that it increases slightly with incident energy then quickly decreases.

*Pair production happens only with high energy photons near a second particle (to conserve momentum again). The photon exchanges a "virtual photon", which is actually a manifestation of the Coulomb interaction, with the extra particle, allowing it to produce a particle-antiparticle pair. The cross section for this goes (approximately for lower energies; for sufficiently high energies this converges to a near-constant value) with: $$\sigma\propto Z^2 \log(k_0-k_{crit}),$$ where $k_{crit}$ for electron-positron pair production is approximately $2m_e$.
The likelihood of each occuring will depend on the mass and charge of the atom (assuming you're scattering off "normal matter") the photon interacts with, but they all follow the same general trend. For example, here is the mass attenuation coefficient by interaction type for copper:

This basically measures how "likely" a material is to interact with photons. Energies with higher attenuation coefficients mean a photon, on average, interacts after having traveled a shorter distance than energies with lower attenuation coefficients. The "dominant" interaction mechanism in this case is simply the mechanism with the highest mass attenuation coefficient, which is just another way of expressing absorption cross section (by mass instead of by particle). In general, for low energies, photoelectric absorption will dominate. For energies on the order of $1$MeV when scattering off common unionized atoms, Compton scattering will dominate, and for high energies, pair production will dominate.
