Which model for a content suggestion in which only some of the items are currently available I am trying to understand the type of model that would be used in a content suggestion scenario where not all of the choices are available at a given time.  For example, when an online movie subscription service suggests a show it does not need to worry about if the content is available because it's unlimited.  A storefront renting DVD's however, does.  My problem is like the storefront where only a certain few of the content items is available at a given time.
For the environment, let there be 1000 pieces of content in total, 100 of which are available at a point in time.
I am considering the pros and cons of approaching this in two way:

use a model where I can ask for a probability for all 1000 pieces of content in one call for the current environment, then check which ones are available.

check which items are available, ask the model for the probability of each.


Both of these seem inefficient. Performance is certainly a consideration as this model will live in an environment where it needs to be very fast.
Are there any models which can account for some of the choices not being currently available?
It is pretty common in recommendation systems to have business constraints to filter against before a final recommendation is made (e.g. checking whether each recommendation is in stock).
One way to manage this is to produce a superset of recommendations (e.g. 100 if you need to produce 10 recommendations), apply your filters (which could drop the number of recommendations down considerably), and then return the top-10 recommendations from the filtered set. So, you may not need to produce the full 1000 item recommendation set each time, but you most likely will need to generate a list which is initially large and filter down.
A potentially helpful link:
https://buildingrecommenders.wordpress.com/2015/11/10/the-components-of-a-recommender-system/