Probability function on k items with different prices Is there a mathematical way to study problems like the following:

I have 3 items $A$, $B$, $C$ and their 3 respective prices $x$, $y$, $z$. How to measure the propensity of a potential customer in selecting a particular item among the three mentioned?

Also some links would be very useful. 
 A: Yes, there is. There are plenty of them actually. Luce's choice axiom is a good start. Assuming all the prices are positive, you can make the following assumption : 
$$P(A)=\frac{x^\alpha}{x^\alpha+y^\alpha+z^\alpha}$$
Where $P(A)$ represents the probability to chose article $A$. If $\alpha$ is positive, the probability to chose an article will be increasing with its price. Maybe you want to use $\alpha<0$. The more expensive an article is, the less likely it is to be chosen.
Note that $\alpha=0$ represents insensitivity with respect to the price.
A more general answer would be to chose $f$, a weighting function (that is, in general decreasing, but you could relax this hypothesis) that associates a weight to a price and generate:
$$P(A)=\frac{f(x)}{f(x)+f(y)+f(z)}$$
But $f$ becomes complicated to estimate. On the other hand, if you have a limited number of observations (you know that $n$ customers faced $k$ products and chose a specific one), you can estimate $\alpha\in\mathbb{R}$ easily with maximum likelihood (or any other method).
