Background Based Conversation (BBCs) have been introduced to help conversational systems avoid generating overly generic responses. In a BBC, the conversation is grounded in a knowledge source. A key challenge in BBCs is Knowledge Selection (KS): given a conversational context, try to find the appropriate background knowledge (a text fragment containing related facts or comments, etc.) based on which to generate the next response. Previous work addresses KS by employing attention and/or pointer mechanisms. These mechanisms use a local perspective, i.e., they select a token at a time based solely on the current decoding state. We argue for the adoption of a global perspective, i.e., pre-selecting some text fragments from the background knowledge that could help determine the topic of the next response. We enhance KS in BBCs by introducing a Global-to-Local Knowledge Selection (GLKS) mechanism. Given a conversational context and background knowledge, we first learn a topic transition vector to encode the most likely text fragments to be used in the next response, which is then used to guide the local KS at each decoding timestamp. In order to effectively learn the topic transition vector, we propose a distantly supervised learning schema. Experimental results show that the GLKS model significantly outperforms state-of-the-art methods in terms of both automatic and human evaluation. More importantly, GLKS achieves this without requiring any extra annotations, which demonstrates its high degree of scalability.