I know ard diagnosis depends on the whole clinical picture. probability-wise, which ards are associated with a nuclear coarse speckled ana pattern?

Depends on other lab: There are a number of rheumatologic diseases that could have that ANA pattern, and it's also possible to have a positive ANA without having a disease. Diagnosis depends on more than just the ANA -- your doctor will probably do other tests, and with all the lab results plus your physical exam, be able to give you a diagnosis.