Appointments shall be on probation for a period to be fixed by the rules of the board. At the expiration of such period of probation, the appointing officer may discharge a candidate at will, but, if he is not then discharged, the appointment shall be deemed complete. The board may strike from any eligible list the name of any candidate which has remained thereon more than one year. After one-third of an eligible list has been drawn, the board may hold another examination to obtain a new list. Any person remaining on the eligible list may retain his rating or, at his option, may enter the test and obtain a new rating which shall supersede his former rating. Immediate notice in writing shall be given by the appointing power to the board of all appointments, permanent or temporary, made in the classified civil service and of all transfers, promotions, resignations or vacancies from any cause in such service, and of the date thereof, and a record of the same shall be kept by the board. When any office or employment is created or abolished or the compensation attached thereto altered, the officer or board making such change shall report it immediately in writing to the board.