While its unlikely that the Serbian government would have ever directly ordered such an assassination, it wouldn't be that hard to have evidence come to light that directly linked the Black hand with Serbia. Have evidence come to light (surviving papers or something like that) linking ranking Serbian generals and/or politicians with the upper echelons of the Black hand, enough to show that the terrorist organization took orders form part of the Serbian government.
Russia would be hard pressed to support regicides and would have to back down. Austria-Hungary, supported by Germany and possibly Italy (would a government backed assassination be considered aggression enough to trigger the triple alliance?) would invade and occupy Serbia (and possibly Montenegro). A new government and probably dynasty (possibly a branch of the Habsburgs) would be installed in one or both of the Serb states with limits placed on the military and probably on diplomatic ties to Russia.
This would be a major diplomatic victory for the Triple alliance and yet another show of weakness for Russian foreign policy, basically establishing permanent Austro-German influence in the Balkans (Romania and Bulgaria were fairly Pro-German, Greece was neutral and Albania a nonentity). However, long-term this would no doubt cause problems between the Entente and Triple alliance and could potentially push the Ottoman empire into an alliance with Britain and France (a fear of becoming dominated by Austria-Hungary and Germany).
On the other hand, with Yugoslav nationalism temporarily defeated, I think Austria would be in a stronger position, sense one of the largest external threats would be removed. In all I think that a defeat of Serbia, without drawing the rest of Europe in, could have the potential to lower the tensions in Europe, if handled correctly.