The last time a Best Picture winner didn't get a Best Director nomination was with Driving Miss Daisy. If Zero Dark Thirty or Argo wins it will be a huuuuuuuuge surprise. Lincoln is the clear favorite at this point though.
Argo and Zero Dark thirty will (almost certainly) not win. A Best Picture winner usually always has a Best Director nominations as well. There are a few exceptions, but it's extremely rare.