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"Natural" vs "non-natural" Distribution
There is no such thing as a "natural probability distribution". Actually, biological system often produce distributions that does not match with commonly used distributions just because the assumptions yielding to these distribution are sometimes poorly met in nature. In other words, many biological variables meet more complicated distribution than the standard uniform, binomial, geometric, beta, exponential, and other distribution you know of.
Of course the gaussian distribution is kind of a special one that is often approximatively reproduced by biological system as a consequence of the central limit theorem.
Some distributions are more used than others but there exist an infinite number of definitions and anyone can construct one. Here is my distribution of the day. $P(x | y,z) = C \frac{y^x - exp(-yz)}{x+z+y}$, where $C$ is a constant of integration to ensure $\int_{-\infty}^{\infty} C \frac{y^x - exp(-yz)}{x+z+y} = 1$. I will call this distribution the "remi.b distribution". I have no idea what kind or process it can model and nobody will probably ever use it but it is a legit distribution.
Developmental mechanism
You can read this post and that post about the developmental mechanism that yield to such bias sex-ratio at birth.
Evolutionary processes
how can the nature know beforehand that boys should be made in excess?
Organisms producing a bias sex-ratio are selected for as they increase the average fitness among their offspring. As such the population is selected toward creating such bias sex-ratio. Organism don't know, they just do.
In order to understand the evolution of sex-ratio a bit better, you should have a look at this post.