Local differential privacy (LDP) is a privacy metric that quantitatively guarantees individual privacy, and many mechanisms have been studied to satisfy LDP depending on data format and use case. Many proposed mechanisms strictly satisfy LDP by perturbing the data considering the worst-case scenario. In this paper, we define functional local differential privacy (FLDP), which is an extension of LDP, and propose a probabilistic disturbing mechanism that satisfies both LDP and FLDP. When data subjects allow disclosure of certain features, the worst-case scenario no longer needs to be considered and the privacy is ensured with less noise. We further propose a FLDP framework to guarantee the privacy of all data in the framework by LDP. Finally, we evaluate the proposed framework through experiments using image data.