Sharing between commercial and Federal incumbent users, such as in the 3.5 GHz band, is expected to increase the availability of spectrum for wireless broadband use. However, the spectrum coordination needed between incumbent and commercial users gives rise to several privacy concerns. This paper analyzes the vulnerability of the incumbent's operational center frequency to disclosure from inference attacks. We evaluate the inherent protection provided by two channel assignment schemes in terms of the time required for an attacker to infer the incumbent's frequency. We account for the activity of secondary users in a dynamically-shared environment. This analysis quantifies privacy for a given secondary load. It also provides an analytical framework to quantify the effectiveness of countermeasures such as limiting the query rate of secondaries..