CHICAGO—As the NBA’s annual Draft Combine kicked off here Thursday afternoon, the Knicks found themselves in an unusual position: Not only do they lack even a single pick in the June 23 draft, they don’t even have a permanent head coach to help conduct an evaluation of the available talent.

Instead, Kurt Rambis, who has held the job on an interim basis since February, was at the Quest Multisport Complex on the west side of Chicago, watching prospects play games of 5-on-5 along with a couple of high-level scouts and assistant...