So it is always best to contact a family member of [the] business for better and faster access. This sentence could be re-written and then it may become clearer why we use "the": So it is always best to contact a family member (contact one of the members of the family who work at the specific family owned business that you will contact in order to receive better and faster access. You contact one of the family members (a family member) at the specific business (the one and only business) where the family member works. If you said "a business" it could be any business, not necessarily the business where the family member works.