You must complete Hao’s mission “Shift Work” to unlock these races. Upon completion of a race, you will have to wait for a text from Hao before the next race is unlocked. This can sometimes take a few days to arrive so do something else in the meantime.
Only Franklin can participate in these races so you can make use of his special during the races. Make sure you get it filled before you go racing to save you a lot of effort later on. It is also wise to enter with a very fast car like the supercars available. The Cheetah or Pegassi Infernus/Vacca are very good choices. They are expensive to fully kit out but it is definitely worth doing because you can easily beat your competition this way.
You will also need a superbike for the last race. The Pegassi Bati or the Dinka Double-T make excellent bikes for this race. Make sure to fully upgrade them as well.