# Probability of transition defined as the the ratio between reflected and incident fluxes

I'm reading a paper (Rapp, 1968) that treats quantum mechanically the problem of a particle $$A$$ "hitting" an harmonic oscillator made of two particles, $$B$$ and $$C$$:

In the limit $$\tilde{x}\to +\infty$$, the solution of the time-independent Schrodinger equation that deals with the relative energy of the system is:

$$\lim_{x\to +\infty} \psi(x,y)=H_I(\tilde{y})e^{-ik_I\tilde{x}}+\sum_{n=0}^\infty a_nH_{n}(\tilde{y})e^{ik_n\tilde{x}}$$

where $$H_n(\tilde{y})$$ are the spatial wavefunctions of the free harmonic oscillator. So, this solution considers the incident wave that accompanies the incident particle $$A$$ and also the resultant reflected waves. The authors claim that the probability of transition from the state $$I$$ to the state $$n$$ is given by the ratio between the $$n^{th}$$ reflected flux and the incident one:

$$P_{I\to n}=\frac{k_n}{k_I}|a_n|^2$$

But why is this probability computed like this? What is the intuition behind this relation?