Determining Confidence Probabilities for Distribution

I have a LSTM neural network that predicts the number of items required in each room for the next time step. So for example for room A, B, C and D the model predicts

• A -> 3 items
• B -> 4 items
• C -> 2 items
• D -> 2 items

where all the items are assumed to be of the same type. The problem I have is how to distribute the items across the rooms when the prediction asks for more items then I have available.

Is there an approach you would suggest where I would be able to determine the distribution based on the confidence level of the number of items in each room? As an example, using the predicted distribution for the ‘rooms’ above where the total number of items predicted to be required are 11:

A -> probability 1 item: 0.9,
2 items: 0.8,
3 items: 0.3

B -> probability 1 item: 0.9,
2 items: 0.8,
3 items: 0.8,
4 items: 0.3

C -> probability 1 item: 0.7,
2 items: 0.2

D -> probability 1 item: 0.7,
2 items: 0.7

if I only have 10 items it would be possible to identify that C has the least probability of needing it thus I would be able to distribute as follows:

• A -> 3 items
• B -> 4 items
• C -> 1 item
• D -> 2 items

Any suggestions or references would be of great help.

Thanks in advance.