In this paper the authors describe multistage stochastic programs in a purely in-distribution setting, i.e., without any reference to a concrete probability space, using the notion of trees in probabilistic sense. They construct a space which is rich enough to carry the outcomes of a process and the evolving information as well. The authors introduce and describe the nested or multistage distance, which is the basic concept of this paper, based on the initial work of the first author [G. P. Pflug, SIAM J. Optim. 20, No. 3, 1406–1420 (2009; Zbl 1198.90307)]. The nested distance is adapted for problems arising in stochastic optimization.