Help - Buying a house - tenants already received a 60-day notice

[Ori Skloot]

Hey folks,

If an owner has given tenants on a month-to-month lease a 60 day notice to terminate tenancy and then I buy that property before that 60 days is up, is the time period still counting down from when the notice was given?  Or, because I am the new landlord, do I have to restart the 60-day notice process?   

For double points, what about an eviction process?  If I buy a property that is in the middle of an eviction, do I have to refile because I'm the new owner, or do I just continue with the timeline of the former owner?  

House is in unincorporated part of Contra Costa County in California.

Thanks for any advice!