# How to get the probability/closeness of a sample belonging to a specific cluster?

I'm new to this so please let me know if my logic of comparing cosine similarity and k-means is incorrect

I got a set of 4 clusters from k-means and now I'm interested in the Cluster No. 1. For this cluster, I take the average of all values for each column and keep it aside.

Now, I have a test sample, for which I run k-means prediction and I get output as 1, meaning it belongs to Cluster No. 1 which is good for me but my use-case here was to calculate that even if that sample didn't belong to Cluster 1, how close was it to falling in that Cluster No. 1

Hence, to resolve this I thought of doing a cosine similarity between my test sample and the one where I take average of all values for each column. Now, in this case, I get a similarity of just 5%

I'm not sure, for my use-case i.e. (Getting the probability/closeness of a sample belonging to a specific cluster) which is a better interpretation for me?

I know I can use the cluster labels as y variables and make multi-class classification model but I want to keep it as un-supervised as possible. Please guide