Let's assume I have two boxes that I want to fill with my stickers. The stickers can have three colors. There can only be one green sticker, only two orange ones, and only five purple ones. Note that I can have them all or only a portion of them.
Now the boxes are to be filled with the stickers. The green sticker is the rarest and so if I have one I want to make sure that it is in the first position in Box 1. The orange stickers are also quite valuable (not as much as the green one but more than a purple one) - hence if I have one I want to make sure that it is in the first box. Depending on the situation:
a) if I have one green and two orange ones, I want them ordered: $\color{green}{\clubsuit}\color{orange}{\clubsuit}\color{orange}{\clubsuit}$ in the first box
b) if I have one green and one orange, I want them ordered: $\color{green}{\clubsuit}\color{orange}{\clubsuit}$ in the first box
c) if I have no green and one or two orange ones, I want them ordered: $\color{orange}{\clubsuit}$ or $\color{orange}{\clubsuit}\color{orange}{\clubsuit}$ in the first box
A similar logic is applied to the purple stickers. They are the least important and so they fill the first box up until there is a place there. If there's no more room in Box 1, then I want to put them in the second box.
A situation where I have $1\color{green}{\clubsuit}$, $2\color{orange}{\clubsuit}$ and $5\color{purple}{\clubsuit}$ can be visualized as seen below:
$$\begin{array}{c|c|c|} & \text{Box 1} & \text{Box 2} \\ \hline \text{Position 1} & \color{green}{\clubsuit} & \color{purple}{\clubsuit} \\ \hline \text{Position 2} & \color{orange}{\clubsuit} & \color{purple}{\clubsuit} \\ \hline \text{Position 3} & \color{orange}{\clubsuit} & \color{purple}{\clubsuit} \\ \hline \text{Position 4} & \color{purple}{\clubsuit} & \color{purple}{\clubsuit} \\ \hline \end{array}$$
Imagine the stickers are distinguishable, like Pokemon cards. And so it looks more like this (or some permutation of it):
$$\begin{array}{c|c|c|} & \text{Box 1} & \text{Box 2} \\ \hline \text{Position 1} & \color{green}{\clubsuit}_1 & \color{purple}{\clubsuit}_1 \\ \hline \text{Position 2} & \color{orange}{\clubsuit}_2 & \color{purple}{\clubsuit}_3 \\ \hline \text{Position 3} & \color{orange}{\clubsuit}_1 & \color{purple}{\clubsuit}_5 \\ \hline \text{Position 4} & \color{purple}{\clubsuit}_4 & \color{purple}{\clubsuit}_2 \\ \hline \end{array}$$
Now, I want to calculate the probability that the particular purple sticker is inside of Box 1 given that I have $x/1\color{green}{\clubsuit}$, $y/2\color{orange}{\clubsuit}$ and $z/5\color{purple}{\clubsuit}$. So that I know the upper limit of the number of stickers of each color.
I'm thinking conditional probability can help here, but I'm not entirely sure how to do it. Does $P(\color{purple}{\clubsuit}_1 | \#\color{green}{\clubsuit}, \#\color{orange}{\clubsuit}, \#\color{purple}{\clubsuit}) $ make sense? This situation is a bit different from what I am used to and so not entirely sure if I can use conditional probability here.
EDIT 1. After giving it some additional thought - does the problem go straight to the following:
$P(\color{purple}{\clubsuit}_1 | \#\color{green}{\clubsuit}, \#\color{orange}{\clubsuit}, \#\color{purple}{\clubsuit}) = \frac{\#\mathrm{Box1} - \#\color{green}{\clubsuit} - \#\color{orange}{\clubsuit}}{\#\color{purple}{\clubsuit}}$ as simple as that and there is no need for conditional probabilities per see?