South had three low probability chances (in order):
1. Trent Affair blows up. This doesn't necessary require the British to go active into warfare with the U.S. The U.S. bought half a million rifles from Enfield just after the Affair, so even an arms embargo would be extremely damaging. Arguing against this is the fact that the UK was buying roughly 40% of its coarse grain from the U.S. at the time and no ready replacement source was available.
2. Jubal Early takes the high ground on day 1 at Gettysburg, forcing Meade to try to dislodge the Army of Northern Virginia from some of the best defensive ground seen during the Civil War. If Meade's forces are mauled Washington is in danger. OR Hill's forces take Little Round Top on Day Two allowing them to roll up Meade's entire line. This puts Lee's forces between most of the Army of the Potomac and Washington. Arguing against this is that even in a mauled state the Army of the Potomac is a strong enough command that, while supported by the forts ringing the Capital, Lee is likely to break his army attempting to carry the fortifications.
3. McClellan wins the 1864 election. This requires a much more negative perception of the war by the electorate of the North (which requires several separate noteworthy POD). The pre-conditions to allow this are extremely low, but still above Zero.
None of these are reasonably possible. None, IMO, have even a 10% chance of occurring, # 3 is 1% or less. Still 1% is a chance. So call it extremely unlikely