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Fog computing is an emerging paradigm that aims to meet the increasing computation demands arising from the billions of devices connected to the Internet. Offloading services of an application from the Cloud to the edge of the network can improve the overall Quality-of-Service (QoS) of the application since it can process data closer to user devices. Diverse Fog nodes ranging from Wi-Fi routers to mini-clouds with varying resource capabilities makes it challenging to determine which services of an application need to be offloaded. In this paper, a context-aware mechanism for distributing applications across the Cloud and the Fog is proposed. The mechanism dynamically generates (re)deployment plans for the application to maximise the performance efficiency of the application by taking the QoS and running costs into account. The mechanism relies on deep Q-networks to generate a distribution plan without prior knowledge of the available resources on the Fog node, the network condition and the application. The feasibility of the proposed context-aware distribution mechanism is demonstrated on two use-cases, namely a face detection application and a location-based mobile game. The benefits are increased utility of dynamic distribution in both use cases, when compared to a static distribution approach used in existing research.