A defendant may file a third-party notice if the defendant wants to—
(a) claim a contribution or indemnity against a person who is not already a party to the proceeding; or
(b) claim relief against a person who is not already a party to the proceeding that—
(i) relates to or is connected with the original subject matter of the proceeding; and
(ii) is substantially the same as some relief claimed by the plaintiff; or
(c) require an issue relating to or connected with the original subject matter of the proceeding to be decided not only as between the plaintiff and defendant but also between either of them and a person not already a party to the proceeding.