If you get preferential treatment, you are treated better than other people and therefore have an advantage over them. Despite her status, the Duchess will not be given preferential treatment. = special. preferential treatment, rates etc are deliberately different in order to give an advantage to particular people
manifesting partiality; "a discriminatory tax"; "preferential tariff rates"; "preferential treatment"; "a preferential shop gives priority or advantage to union members in hiring or promoting"