predicting probability distribution for time series I have time series of several variables. Just in one specific case one variable is linear combination of the rest.

I want to predict probability distribution (that is not only best estimate but estimates with probability of that happening) of future value of variables. I want to see when probability of small interval of possible outcome is high.

A priory I don't know rules of the game how variables evolve and inter-depend. 

What is the tool to best do such prediction and how easy is it? Will scikit-learn do? Maybe neural networks?

ADDED based on answer:

As I've understood, time series theory data science assumes random walk, however I assume variables are at least partly moved by free will of players of the game under some a priory unknown to me constraints and goals.

Should statistical solution advised work in such case? Can data predict reversal of possible current trend?
Yes, you can use scikit-learn for this use case. You may find this tutorial useful.