Adequate capacity planning of substations and feeders primarily depends on an accurate estimation of the future peak electricity demand. Traditional coincident peak demand estimation is carried out based on the empirical metric, after diversity maximum demand, indicating individual peak consumption levels and demand diversification across multiple residents. With the privilege of smart meters in smart cities, this paper proposes a datadriven probabilistic peak demand estimation framework using fine-grained smart meter data and sociodemographic data of the consumers, which drive fundamental electricity consumptions across different categories. In particular, four main stages are integrated in the proposed approach: load modeling and sampling via the proposed variable truncated R-vine copulas method, correlation-based customer grouping, probabilistic normalized maximum diversified demand estimation, and probabilistic peak demand estimation for new customers. Numerical experiments have been conducted on real demand measurements across 2639 households in London, collected from Low Carbon London project's smart-metering trial. The mean absolute percentage error and the pinball loss function are used to quantitatively demonstrate the superiority of the proposed approach in terms of the point estimate value and the probabilistic result, respectively.