Its not clear, based on your description, what you want to do in every possible case.
For example - “What he writes in input determinates options he gets”. Does that mean that you are testing for specific values in the text field? If so, how many different choices (perhaps you should be using a select/option menu instead) and what are the different sets of options that are available for each text value?
Do you want a <div>
for each select menu or just one total? When do you want the <div>
to be shown and when do you want to hid it?
This will require an on change event for the text input, that will cause the first, blank option to become selected, on every change made to the text input. You could write more complicated code to ‘remember’ that a change occurred in the text input, perhaps just a counter, then only change the first, blank option to become selected on blur (loss of focus) of the text input, if the corresponding counter is not zero.