The CAP theorem is a fundamental result that applies to distributed storage systems. In this paper, we first present and prove two CAP-like impossibility theorems. To state these theorems, we present probabilistic models to characterize the three important elements of the CAP theorem: consistency (C), availability or latency (A), and partition tolerance (P). The theorems show the un-achievable envelope, i.e., which combinations of the parameters of the three models make them impossible to achieve together. Next, we present the design of a class of systems called PCAP that perform close to the envelope described by our theorems. In addition, these systems allow applications running on a single data-center to specify either a latency SLA or a consistency SLA. The PCAP systems automatically adapt, in real-time and under changing network conditions, to meet the SLA while optimizing the other C/A metric. We incorporate PCAP into two popular key-value stores -- Apache Cassandra and Riak. Our experiments with these two deployments, under realistic workloads, reveal that the PCAP system satisfactorily meets SLAs, and performs close to the achievable envelope. We also extend PCAP from a single data-center to multiple geo-distributed data-centers.