In this paper, we embed metric space endowed with a convex combination operation, named convex combination space, into a Banach space and the embedding preserves the structures of metric and convex combination. For random element taking values in this kind of space, applications of embedding are also established. On the one hand, some nice properties of expectation such as representation of expected value through continuous affine mappings, the linearity of expectation will be given. On the other hand, the notion of conditional expectation will be also introduced and discussed. Thanks to embedding theorem, we establish some basic properties of conditional expectation, Jensen's inequality, convergences of martingales and ergodic theorem.