Highly photoconductive thin films of inorganic-capped PbS nanocrystal quantum dots (QDs) are reported. Stable colloidal dispersions of (NH4)3AsS3-capped PbS QDs were processed by a conventional dip-coating technique into a thin homogeneous film of electronically coupled PbS QDs. Upon drying at 130 °C, (NH4)3AsS3 capping ligands were converted into a thin layer of As2S3, acting as an infrared-transparent semiconducting glue. Photodetectors obtained by depositing such films onto glass substrates with interdigitate electrode structures feature extremely high light responsivity and detectivity with values of more than 200 A/W and 1.21013 Jones, respectively, at infrared wavelengths up to 1400 nm. Importantly, these devices were fabricated and tested under ambient atmosphere. Using a set of time-resolved optoelectronic experiments, the important role played by the carrier trap states - presumably localized on the arsenic-sulfide surface coating - has been elucidated. Foremost, these traps enable a very high photoconductive gain of at least 200. The trap state density as a function of energy has been plotted from the frequency dependence of the photoinduced absorption (PIA), whereas the distribution of lifetimes of these traps was recovered from PIA and photoconductivity (PC) phase spectra. These trap states also have an important impact on carrier dynamics, which led us to propose a kinetic model for trap state filling that consistently describes the experimental photoconductivity transients at various intensities of excitation light. This model also provides realistic values for the photoconductive gain and thus may serve as a useful tool to describe photoconductivity in nanocrystal-based solids.