One in five hundred and twelve if each year's schedule is independent of other years. It would be exactly the same for any pattern of 9 home/aways that you choose but that's not the right question because it being equally unlikely doesn't indicate that the draws are truly random.
The right question is, "What are the odds of that 9-year home/away streak containing no home games?" Every year this continues the odds of it happening halve. It's already far beyond outrageous.
