Using a custom formula for validation never creates a dropdown. Dropdowns are available only for lists of values that are either entered directly into the validation rule, or are contained elsewhere in a sheet ("list from a range").
Possible workaround: use "list from a range" validation rule, referring to a range in which you use some formulas to compute the available options.
Example: cell B3 has validation rule saying "list from the range P3:R3". Cell P3 has the formula =if(isblank(A3), "", {"aa", "bb", "cc"})
. So, if A3 is nonempty, than the range P3-R3 contains "aa", "bb", "cc", and these values appear in the dropdown in B3. Otherwise it'sthe range is blank, and so is the dropdown.