Distribution of percentage depending on the price of the case and things in it?

Question

Probability theory

Hello! I'm doing the opening of money cases (chests) for one educational project. So, is there such an option, where the percentage of loss between items is distributed evenly, depending on the price of the case (chest)?
For example:
The price of a case is 50 rubles
Things in it:
1 - 10 rubles. (30%)
2 - 25 rubles. (25%)
3 - 40 rubles. (20%)
4 - 50 rubles. (15%)
5 - 65 rubles. (10%)
If the price of the case is increased to 65 rubles, then:
1 - 10 rubles. (10%)
2 - 25 rubles. (25%)
3 - 40 rubles. (30%)
4 - 50 rubles. (20%)
5 - 65 rubles. (15%)
I wrote approximate percentages, but I hope you get the point.

Answer 1

there is a solution: https://ru.wikipedia.org/wiki/Poisson_Distribution
The numbers are taken from the last example with a case for 59 rubles.
expectation lambda = 59
we calculate p(k) using the formula from the wiki: p(0), p(1),.. p(2500)
further P0=p(0)+...p(9)
P1=p (10)+...+p(29)
P2=p(30)+...+p(49)
...
P13=p(1500)+...+p(2499)
P14=1-P1 -P2-P3-...-P13
further, P0 (empty win) does not fall out in our case, so we adjust the rest of the odds:
P1=P1+P0/14
P2=P2+P0/14
...
P14=P14+P0 /14
You can check if the sum P1+...+P14 should be =1, to get it as a percentage we multiply by 100%
The seller wins by "rounding" the price of the item. Those. according to the P13 formula, these are the chances of winning from 1500 rubles. up to 2499 rubles, but in fact the winnings will be only 1500 rubles.
This is just one of many variations of the formula.
PS oops... the moderator accepted the version of the question without unnecessary tags, but the question itself remained in the old version... it turned out unsuccessfully.

Answer 2

Two equations:
1. Dependence on the cost of the item number of the case with a 30% probability.
2. Cycloid distribution of objects in terms of probabilities. (30% - at the highest point: 90°)