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Edge caching (EC) decreases the average access delay of the end-users through caching popular content at the edge network, however, it increases the leakage probability of valuable information such as users preferences. Most of the existing privacy-preserving approaches focus on adding layers of encryption, which confronts the network with more challenges such as energy and computation limitations. We employ a chunk-based joint probabilistic caching (JPC) approach to mislead an adversary eavesdropping on the communication inside an EC and maximizing the adversary's error in estimating the requested file and requesting cache. In JPC, we optimize the probability of each cache placement to minimize the communication cost while guaranteeing the desired privacy and then, formulate the optimization problem as a linear programming (LP) problem. Since JPC inherits the curse of dimensionality, we also propose scalable JPC (SPC), which reduces the number of feasible cache placements by dividing files into non-overlapping subsets. We also compare the JPC and SPC approaches against an existing probabilistic method, referred to as disjoint probabilistic caching (DPC) and random dummy-based approach (RDA). Results obtained through extensive numerical evaluations confirm the validity of the analytical approach, the superiority of JPC and SPC over DPC and RDA.