Name the deformity: the finger shows a swan-neck, PIP hyperextended and DIP flexed. Spotting this plus the line PIP involved, DIP spared is the whole answer.
Joint map as a sieve: rheumatoid arthritis loves the MCP and PIP and spares the DIP, exactly the pattern given, and its deforming synovitis is what creates swan-neck and boutonniere fingers. So this is RA.
Cross off the rest by their joint signature: osteoarthritis hits the DIP (Heberden) and PIP (Bouchard) with bony nodes, not soft-tissue swan-neck, and it does not spare the DIP. Psoriatic arthritis prefers the DIP with nail pitting and a pencil-in-cup look. Ankylosing spondylitis is a spine and sacroiliac disease, not a finger deformity. Rheumatoid arthritis is the fit.
Ref: Medscape.