(a) A sheriff, undersheriff, or deputy sheriff, employed in that capacity, of a county, a chief of police of a city or chief, director, or chief executive officer of a consolidated municipal public safety agency that performs police functions, a police officer, employed in that capacity and appointed by the chief of police or chief, director, or chief executive of a public safety agency, of a city, a chief of police, or police officer of a district, including police officers of the San Diego Unified Port District Harbor Police, authorized by statute to maintain a police department, a marshal or deputy marshal of a superior court or county, a port warden or port police officer of the Harbor Department of the City of Los Angeles, or an inspector or investigator employed in that capacity in the office of a district attorney, is a peace officer. The authority of these peace officers extends to any place in the state, as follows:

1. (1) As to a public offense committed or for which there is probable cause to believe has been committed within the political subdivision that employs the peace officer or in which the peace officer serves.
2. (2) If the peace officer has the prior consent of the chief of police or chief, director, or chief executive officer of a consolidated municipal public safety agency, or person authorized by that chief, director, or officer to give consent, if the place is within a city, or of the sheriff, or person authorized by the sheriff to give consent, if the place is within a county.
3. (3) As to a public offense committed or for which there is probable cause to believe has been committed in the peace officer’s presence, and with respect to which there is immediate danger to person or property, or of the escape of the perpetrator of the offense.