Item Based Collaborative Filtering with No Ratings
There might be different ways to do that, like considering implicit ratings like views or clicks.

But basically, you can consider a rating of 1.0 for each user-item pair you have.

This way, your prediction will be between 0 and 1 which you can consider similar to a click prediction probability. 


0 being the probability on not having a click or the item by a user 
1 being the probability that a click would be made. 


You can also set a threshold where you can drop a recommendation at a certain limit of your prediction level. 

E.g. Let's say an user alpha has the following recommendations with a threshold of 0.7


i1 , 0.87
i2, 0,75
i3, 0,6


You can drop the i3 recommendation since you don't consider it good enough. 

Nevertheless, the parameter of your recommendation engine must be determined of course with the help of your evaluation metrics. 

Considering software solutions, I use Apache Spark MLlib with Scala as a base for my recommendation engine algorithms where you can compute item cosine similarity easily per example where you are using in-house implementation or an approximation with the DIMSUM algorithm. 

I hope this helps!