For solving your problem you need to use trigger with corresponding SQL statement for each action: insert, update, delete. As variant you can use something like this (Note, I left only two columns from your example for readability, so modify your trigger as you need):
create or replace trigger "PASSENGERS_BACKUP_TIUD"
after insert or update or delete on "PASSENGER"
for each row
begin
if inserting then
insert into "PASSENGER_BACKUP" (pb_id, pb_first_name)
values (:NEW.pb_id, :NEW.pb_first_name);
elsif updating then
update "PASSENGER_BACKUP"
set pb_id=:NEW.pb_id, pb_first_name=:NEW.pb_first_name
where pb_id=:NEW.pb_id;
elsif deleting then
delete from "PASSENGER_BACKUP"
where pb_id=:OLD.pb_id;
end if;
end;
Also you can see work of this trigger in action on SQL Fiddle.