If property is titled in the name of the living trust, it is not subject to probate in California. The same is true if it's located in another state - but make sure it's not simply listed on "Schedule A" (or some other schedule) as trust property ... that is generally sufficient to transfer California-based assets to a living trust, but it's not sufficient in other states.
If property has named beneficiaries (such as IRAs or insurance policies), or if it's held in a POD/TOD account with named POD beneficiaries, that isn't subject to probate either.
Keep in mind that just because property is not subject to probate does NOT mean it's exempt from any applicable estate taxes.
The information you obtain at this site is not, nor is it intended to be, legal advice. You should consult an attorney for individual advice regarding your own situation.