Is a defendant's actual time in jail credited against any new term of imprisonment imposed as a condition of probation for the same offence?

"[W]hen the defendant has been in custody . . . all days of custody . . . including days served as a condition of probation . . . shall be credited upon his or her term of imprisonment . . . ." ( 2900.5, subd. (a).) Thus, "actual time previously served in county jail, including time served as a condition of probation" is "credited against any new 'term of imprisonment' served in the county jail for the same offense, including any new jail term imposed as a condition of continuing or reinstating the defendant on probation." (People v. Arnold (2004) 33 Cal.4th 294, 300-301 (Arnold).)