The logistic transformation applied to a d-dimensional normal distribution produces a distribution over the d-dimensional simplex which can sensibly be termed a logistic-normal distribution.
Following is a diagram from Brendam O’Connor.
For example, when you throwing an uniformity distributed coin.
The probability of getting a head is p(x)= (Chances for) / (Total chances) .
The odds is given as: (Chances for) : (Chances against) . where (total chances) = (Chances for) + (Chances against)
Logistic-normal distributions:Some properties and uses. Biometrika(1980) By J. AITCHISON AND S.M.SHEN