Research on commutativity degree has been done by many authors since 1965. The commutativity
degree is defined as the probability that two randomly selected elements in a group commute. In this
research, an extension of the commutativity degree called the probability that an element of a group
fixes a set Ω is explored. The group G in our scope is metacyclic 3-group and the set Ω consists of a
pair of distinct commuting elements in the group G in which their orders satisfy a certain condition.
Meanwhile, the group action used in this research is conjugation. The probability that an element of G
fixes a set Ω, defined as the conjugation degree on a set is computed using the number of conjugacy
classes. The result turns out to be 7/8 or 1, depending on the orbit and the order of Ω
