Validating a US mailing address against an authoritative database

Question

I have the following business requirements to authenticate a user on a web service using his / her supplied name and mailing address:

Here are the requirements:

1. Ask a user to supply his/her first and last name,
2. Look up in an authoritative private database for an exact match, if yes
3. Ask the user to supply their mailing address
4. Look up in an authoritative database for the mailing address using first,last name via exact match, if yes
5. Calculate a statistical probability on whether the user supply, and database extracted, address matches (value is between 0 (definitively no), 1 (exact match))
6. A probability score of 80% shall be considered as "USER AUTHENTICATED"

I am challenged on meeting requirements #5 and #6.

I searched through a few posts here. Although there are quite a few regarding mailing address validation, but none that IMHO quite meet these requirements. For example, I see posts that validate user entered mailing addresses against Google, Yahoo and USPS supplied web services by calling a specific API. The authoritative database, in my case, is supplied as a private database. Then we have the probability score requirement #6 to meet.

Is there an existing web service which I can pass two strings, both in a format of a USA mailing address, and return a probability on a match as described? And in a more general sense, passing any two strings (e.g. names) and returning the same? Has anyone else had a similar requirement, and how did you meet it? I looked at AWS and Google Cloud Service briefly today and didn't quite see a clear implementation path.

Thanks in advance for any assistance.