How to combine two update queries having different set and where clause?

I don't see a nice clean way of combining these two update statements, because the logic in the WHERE clause does not agree. However, we can retain the common condition j = 'j1' in the WHERE clause, and then use a CASE expression to handle the a assignement:

UPDATE tbl_priority
SET a = CASE WHEN priority = '1' THEN 1 ELSE a END,
    g = 1
WHERE j = 'j1'

Note that this is not ideal because we have a branch of the CASE expression which assigns a back to itself. This by itself should not cause a particular record to show up as having been modified though.