Why would one plane in this picture not have gear down yet?
Why does the 747 not have its gear down yet?

Based on the image it is hard to say how far these aircraft are from the runway. The 747 could still be be quite far from the runway and thus does not need to have its gear down yet.

The 747-400 FCOM (NP.21.47 Normal Procedures) says:


  At glideslope alive, call:
  
  
  "GEAR DOWN"
  "FLAPS 20"
  


It looks like the 747 in the picture has already intercepted the glideslope, but this is hard to say from this perspective. Also, operators may have different rules for when to lower the gear.

Then why does the third aircraft already have its gear down?

The most probable reason for this is drag. A flight crew may choose to lower the gear earlier than necessary to reduce its speed. ATC could have instructed this aircraft to fly at a lower speed for spacing and the crew then dropped the gear, which adds significant drag. This is pure speculation, of course.