Traditional information-theoretic privacy uses the mutual information rate as a metric of privacy for protecting the input data stream sent by participating users; a low information rate implies that the entire input data stream cannot be correctly inferred from the output with high probability. In many applications such as smart metering, however, the private event (e.g., whether the user is having dinner within a particular time slot) that a user does not wish to reveal may only be associated with part of the data stream, which can still be inferred correctly by adversaries under a low information rate. To this end, we propose a new information-theoretic metric that can provide event-based privacy guarantees. As a case study, we consider the problem of protecting the privacy in user's home energy usage profile with the aid of an internal energy storage device (e.g., a rechargeable battery). Through charging and discharging, the energy storage device is capable of altering the real-time energy usage profile and masking distinctive patterns that may be of interest to adversaries. We evaluate the new privacy metric under the best-effort control policy, which tries to keep the reported energy usage constant through compensation from the storage device. Through simulations, we show that the new privacy metric can be computed numerically and gives a nontrivial privacy guarantee.