Consider a vector, for example (5, -0.5, 3, -2). We want to find a transformation such that the transformed vector represents a distribution: each component is between 0 and 1 and the components add up to 1 (so that they can be interpreted as probabilities). Each probability should reflect the original value in magnitude (for example, 5 should be associated with the highest probability). An easy solution is found in two steps. We will try to transform the original vector into a vector with positive components and these new components will reflect the dimensions of the original ones. To do this, we have to find a function f to transform components.