In the state of California if a person on probation shares a room with someone not on probation and that person not on probation has a safe do they have the right to search that safe?

Not unless the owner of the safe has previously agreed, perhaps by signing some sort of document waiving his or her privacy rights as a condition to the probationer's release. If the probation officer or police demand that the owner of the safe open it so that they can search it, just say "no". If so, they could perhaps take the probationer into custody and seek to revocate his or her probation. But they would not have the right to search the safe.