It gets even more interesting if you go back to the last Ice Age. Then the Ob RIver, which normally flows into the Arctic Ocean, was obstructed by the vast polar ice cap, it's basin flooded and then overflowed to the south into the Aral Sea whose basin, in turn, flooded and overflowed into the Caspian basin, which -- in turn -- overflowed into the Black Seea via the River Don. This went on long enough to flush all the salt water out of the Caspian. (What happen to the Black Sea is even more interesting, but too long to narrate here.)

So all the salinity in the current Caspain has accumlulated since the last Ice Age through evaporation of the once flooded basin and waters that have flowed into it since from, for example, the Volga RIver.