I feel like this question rather belongs in the History StackExchange.
That being said, one can still speculate on the most plausible outcome of a refusal on the German Empire's part to back up Austria-Hungary in 1914.
First, lets provide some preliminary context :
By 1914, almost all European nations were involved in a complex maze of alliances, pacts and mutual assurances. This was because the rivalries between the different nations (France and Germany following their war in 1870 ; UK and Germany competing for naval dominance ; Germany challenging other nations' role as colonial powers) created a tense, explosive atmosphere in foreign affairs.
Eventually, two opposing sides crystallized, born from the need to seek mutual allies against the rivaling coalition : Germany, Austria-Hungary and (initially) Italy on one side, and France, Great-Britain and Russia on the other.
The respective system of alliances played out that way : Austria-Hungary declared war on Serbia. Russia, stemming from (or pretexting) a necessity to help a fellow slavic nation (and probably to challenge Austria-Hungary), then declared war on the Austrians. This in turn caused Germany to declare war on Russia as was supposed to happen based on their alliance with Austria-Hungary, only for the conflict to further escalate like we know it.
With Germany suddenly removed form the equation, it is fairly likely that the conflict would have stayed mostly regional, and would have been fought out between Russia and Austria-Hungary only.
France would probably not have joined the fight, because France's primary interest was to counter (and take revenge on) Germany. 714
With Germany out of the fight, there is little reason for France to go to war. Likewise, Great-Britain would have most likely stayed out of the war, since the lack of a German invasion of Belgium would have left them with no casus belli. Same reasoning for the US and the lack of German submarine warfare.
This leads to the conclusion that the war would have stayed mainly local, with possible exception of the Ottoman Empire which would have a clear interest in helping the Austrians fight the Russians (for territorial reasons). As for the winner, it's pretty hard to predict. If I remember correctly Austria-Hungary irl had a difficult time fighting Russia, but on the other hand Russia suffered a revolution in 1917 which immediately terminated its ability to continue fighting in the war. 454