Predicting probability for each tag given already chosen tags
welcome to ML and data science. This is a classic situation where a RNN would be usefull. You could either train one from Keras yourself which would help you learn and get a better model but might take more time. Or you could use a more pre-made soloution if this is your first project maybe something like TextGenRNN (will still recquire a bit of modification).

RNN theory

Examples in python

More examples

TextgenRNN Library