The time that it takes to probate an estate varies on the particulars of the specific estate as well as the jurisdiction.  Typically, it can takes about 6-12 months.  Again, however, it depends.

As for your grandmother's inheritance, since she outlived the testator (ie the person who made the Will), if she dies before the state is distributed, her estate will inherit. 

Note:  Sometimes a Will will stipulate that a beneficiary must survive the testator for a certain period of time (usually about 30 days or so).  If they do not, then in that case the inheritance is forfeited.