Contact the probation department in California and advise them of the move. They should transfer the probation to the county where the child will be residing and they should pick up the probation there. They wil tell you what documentation and steps are needed.
Ms. Burgess is correct, however it might be a bit more complicated in that you are moving to another state and not another county within California. It likely will not be a problem for your California county in that is one less person they need to supervise. The other state might not be thrilled as much, both most likely will cooperate. If the terms of your child's probation are not particularly onerous it should not be a problem at all. In terms of time, probably the amount of time it takes for the probation department to make the call to the other state and get approval then going to court to have the probation effectively transferred by the Judge.
To transfer probation from one state to a sister state, the probation department first needs to be advised of the intent to move and they will want a specific address to where the minor will be living. They need to prepare a request via the Interstate Compact on Placement of Minors with the receiving State. (Bureaucratic blah, blah, blah. Could include a home study) It is most always approved. However, it can take months before a home study is done and the paperwork being back in the hands of the sending State.