We experimentally investigate the evaporation of very volatile liquid droplets (Novec 7000 Engineered Fluid, chemical name hydrofluoroethers HFE-7000) in a turbulent spray. Droplets with diameters of the order of a few micrometres are produced by a spray nozzle and then injected into a purpose-built enclosed dodecahedral chamber filled with air containing various amounts of water vapour. The ambient temperature and relative humidity in the chamber are carefully controlled. We observe water condensation on the rapidly evaporating droplet, both for the spray and for a single acoustically levitated millimetric Novec 7000 droplet. We further examine the effect of humidity, and reveal that a more humid environment leads to faster evaporation of the volatile liquid, as well as more water condensation. This is explained by the much larger latent heat of water as compared with that of Novec 7000. We extend an analytical model based on Fick's law to quantitatively account for the data.