A classical algebraic probability space is a unital combative and associative algebra together with a unit preserving linear functional, called expectation, to the ground field. Such a space always come with certain symmetry of expectation, which a resolution leads to the notion of homotopy probability space. We show that there is underlying a formal and Z-graded affinely flat structure (formal based supermanifold which tangent space has torsion-free and flat formal Z-graded affine connection), which flat coordinates determine the law of random variable up to finite ambiguity.