How did the alliances turn a small conflict into a big war?

Russia has formed an alliance with Serbia as a fellow Slavic nation and Germany with Austria-Hungary as part of the Triple Alliance. Russia announced that they would be backing up Serbia when they went to war with Austria-Hungary and in retaliation Germany announced war on Russia whilst beginning movement towards France and Belgium. This brought the French army into the war; ready to fight a German invasion. Germany declared war on France and invaded Belgium. With the German's still in Belgium Britain declared war on Germany as a member of the Triple Entente (Britain, France and Russia) and Austria declared war on Russia.