Unlike Earth and Venus, Mars with a weak gravity allows an extended corona of hot species and the escape of its lighter constituents in its exosphere. Being the most important reaction, the dissociative recombination of O₂⁺ is responsible for most of the production of hot atomic oxygen deep in the dayside thermosphere/ionosphere. The investigation of the Martian upper atmosphere is therefore complicated by the change in the flow regime from a collisional to a collisionless domain. Past studies, which used simple extrapolations of 1-D thermospheric/ionospheric parameters, could not account for the full effects of realistic conditions, which are shown to be of significant influence on the exosphere both close to and far away from the exobase. In this work, the combination of the new 3-D Direct Simulation Monte Carlo kinetic model and the modern 3-D Mars Thermosphere General Circulation Model is employed to describe self-consistently the Martian upper atmosphere at equinox for solar low conditions. For the first time, a 3-D analysis and shape of the Martian hot corona is provided, along with density and temperature profiles of cold and hot constituents as functions of position on the planet. Atmospheric loss and ion production (found to be more than an order of magnitude lower than the neutral escape), calculated locally all around the planet, provide valuable information for plasma models, refining the understanding of the ion loss, atmospheric sputtering, and interaction with the solar wind, in general.