Paul is not making a distinction between believers and non-believers.
In context Paul is making the case of the absolute necessity of the the Resurrection, against the false teachers stating it did not happen.
Now I make known to you, brethren (15:1).
For I delivered to you as of first importance what I also received, that Christ died for our sins according to the Scriptures, 4 and that He was buried, and that He was raised on the third day according to the Scriptures (1 Corinthians 15:3-4).
and you will see he continues to make his case...
...and that He appeared to Cephas, then to the twelve. 6 After that He appeared to more than five hundred brethren at one time, most of whom remain until now, but some have fallen asleep; 7 then He appeared to James, then to all the apostles; 8 and last of all, as it were to one untimely born, He appeared to me also. (1 Corinthians 15:5-8).
I think we forget "the times" when we read scripture... this was all so new to them, they did not have a Bible to reference.