Astrophysical objects capable of hadronic acceleration to relativistic energies have long been believed to be sources of astrophysical neutrinos. Nevertheless, the long exposure neutrino sky map shows no significant indication of point-like sources so far. This may point to flaring objects or a large population of faint, steady sources as origins of this flux. The spatially and temporally 3σ correlated observations of the flaring gamma-ray blazar TXS 0506+056 and a high-energy neutrino detected by IceCube in September 2017, is a result of a Neutrino Target of Opportunity (NToO) program in which all currently operating imaging atmospheric Cherenkov telescopes (IACTs) take part and represents the most compelling evidence for a high-energy neutrino point source to date. The case for TXS 0506+056 being a neutrino source was made stronger by evidence of a 5-month long neutrino flare in 2014-2015. The Cherenkov Telescope Array (CTA) will be the next-generation ground-based gamma-ray observatory. In this work, we investigate the detection probability for the very-high-energy gamma-ray counterparts to neutrino sources from the populations simulated by the FIRESONG software to resemble the diffuse astrophysical neutrino flux measured by IceCube. We scan over parameters that can be used to describe the populations such as luminosity and density (density rate) for steady (flaring) objects. Several CTA array layouts and instrument response functions are tested in order to derive optimal follow-up strategies and the potential science reach of the NToO program for CTA. We find that CTA has a very high per-alert probability of detecting a steady source counterpart in certain parameter space regions. For the blazar flares resembling the neutrino flare of TXS 0506+056 in 2014-2015, CTA will detect more than 30% of the sources in 30 minutes of observation. We also investigate the effect of higher night sky background and the initial CTA Alpha layout on the detection probability.