The short answer is because the Italians themselves had defenestrated Mussolini and the Fascists before fighting alongside the Allies in a civil war to take their country back from Nazi Germany.
The long answer is that Italy was occupied by the Allied forces after World War II, but that it was a much more kind occupation - centered more around recovery - than what had faced Germany and Japan, with a lot of it having to do with the fact that Italy had fought with the Allies as co-belligerents. After Mussolini was arrested under order by Victor Emmanuel III, the Italians were still de facto allies of Germany - with assurances given to Hitler by the King that Italy had no intention of leaving the Axis alliance - but that was very shortly concluded with a minor amount of arm wringing by the Allies on new Prime Minister Badoglio which resulted in the Armistice of Cassibile on 3 September 1943 in which Italy surrendered to the Allies. The Armistice was announced on 9 September in a very poorly worded message that led to a high level of confusion in which Italian units were left with no orders (many thinking that the war was over), and most importantly no help to resist against the German's who immediately launched a counter attack against imminent Allied invasion.^1
The Germans quickly swept in occupying all the way down to Naples - where an insurrection of the people was the only thing that allowed the Allies to gain a toehold.^1 With very short order they liberated Mussolini from jail (the story being that the jailers saluted the German glider troops that came to rescue him), and created the puppet state of the Italian Social Republic (also known as the Salò Republic) which claimed the entirety of Italy, but in effect controlled no further south than Rome. Italian soldiers which had surrendered to the Germans were not treated well at all, being deported back to Germany for forced labor ^1, while the Italian people under the Salò Republic weren't treated much better by the Germans either (Germany is alleged to have started a Malaria epidemic in the Lazio region for example^2), and destroying countless archives in response to partisan resistance movements. The recognized Italian government (that headed by King Victor Emmanuel III and Prime Minister Pietro Badoglio) had fled south to Brindisi, where they declared war on Germany on 13 October 1943 with the left over units still loyal to the King coming under command of the Allies.^3 Partisan resisters were at times invaluable towards the allied effort in the liberation^2 and in quelling any post-war form of resistance against the soldiers of the Salo Republic^4. The Salò Republic would be capitulated by the Germans on 2 May 1945, shortly before the Germans themselves surrendered.
Now the Italian country was in an interesting situation in dealing with both their invasion and liberation. Allied Military Governments were set up in each of the areas that had been liberated, to be transferred to Italian control once the situation had been stabilized - with most areas being transferred out of AMG control by the end of 1944. With the outlawing of the Fascist party, Italy did undertake a period similar in scope to the German de-nazification while inspectors from the South accessed the remaining soldiers and bureaucracy to the North to understand what they did under the Salò regime (and thus if they were capable of continuing in service to the legitimate government)^4. The British and the Americans, meanwhile, grateful for support during the Italian Campaign forwent any reparations during peace settlements^1 and instead rewarded the ravaged country with billions in aid. The crimes of the Fascist regime were in fact seen as just that, crimes of a regime that had been ousted and then actively rebelled against. Benedetto Croce actually played an instrumental role in convincing not just the Italians themselves, but foreign powers that Italy had been just as much of a victim of the Fascists as other countries had^1. The Italian people then took the sword to the monarchy itself, viewing it as having collaborated with the Fascists and leading the country to the current state of ruin that it found itself in^1 (this historiography is much debated, with recent scholarship bringing the idea that the Italian people were passive in disrepute^5) The monarchy was ousted by constitutional referendum on 2 June 1946, to be replaced by the current Italian Republic.
Italy did face the loss of the great majority of it's overseas empire in the 1947 Paris Peace Treaties, along with much of the territory it had taken during the years of it's active participation as a member of the Axis.^1 Much to the chagrin of Charles De Gaulle and the French, Italy only faced a minor readjustment of it's border with France. The only area that remained under occupation and control of the Allies at this point was Trieste, before it's fate was decided by referendum in 1954.