How to handle columns with large/infinte values in dataset for ML classification
Depends a bit on the model you are going to run. I will explain a bit for Linear Models and for Decision trees ensembling (gradient boosting and random forest)

Decision tree

Not much to do, when the tree is built each branch will choose a split. If there is any information gain with a large value, it will choose it and make a split.

Some implementations, as catboost have a quantization in it. The split could be done eventually in something like 95% quantile and that will work with large values.

Generalized Linear Models

You will need to change this. My suggestion is creating a feature based in the values of the column (if df.col1> 9999: 1 else 0).
And then Winsorizing by a certain threshold.