Understanding the formation and evolution of our Galaxy requires accurate distances, ages, and chemistry for large populations of field stars. Here, we present several updates to our spectrophotometric distance code, which can now also be used to estimate ages, masses, and extinctions for individual stars. Given a set of measured spectrophotometric parameters, we calculate the posterior probability distribution over a given grid of stellar evolutionary models, using flexible Galactic stellar-population priors. The code (called StarHorse) can accommodate different observational data sets, prior options, partially missing data, and the inclusion of parallax information into the estimated probabilities. We validate the code using a variety of simulated stars as well as real stars with parameters determined from asteroseismology, eclipsing binaries, and isochrone fits to star clusters. Our main goal in this validation process is to test the applicability of the code to field stars with known Gaia-like parallaxes. The typical internal precisions (obtained from realistic simulations of an APOGEE+Gaia-like sample) are {˜eq } 8 {per cent} in distance, {˜eq } 20 {per cent} in age, {˜eq } 6 {per cent} in mass, and ≃ 0.04 mag in AV. The median external precision (derived from comparisons with earlier work for real stars) varies with the sample used, but lies in the range of {˜eq } [0,2] {per cent} for distances, {˜eq } [12,31] {per cent} for ages, {˜eq } [4,12] {per cent} for masses, and ≃ 0.07 mag for AV. We provide StarHorse distances and extinctions for the APOGEE DR14, RAVE DR5, GES DR3, and GALAH DR1 catalogues.