I can't speak to any odds of soldiers surviving the entire war, but I know that there were soldiers who have done it.

Hans Von Luck is the one that comes to mind although he technically was an officer, but he did spend a significant amount of time on the front and fought in almost every major theater of WWII including Poland, France, Russia, Germany, and Africa. I'm unclear on if he fought in Sicily or Italy , but I don't think he did. If you want to learn more about him I'd suggest Panzer Commander which covers his time during the war. Take it with some measure of skepticism though, it's written well after the end of the war and of course Luck may have inflated some incidents for good measure.

Sorry if that's not the type of thing your looking for, but I can assure you that Luck was far from the only German soldier who survived the entire war.

Germany's losses increased exponentially during the war.

They were very light in 1939 and 1940. They increased substantially in 1941; though kill ratios against the Red Army were about as good as against Poland or France, the magnitudes were far bigger.

Then a further increase in 1942-43.

Then an absolute step change in 1944, when they decisively lost control of the air on the Eastern Front, and for the first time the Soviets began to execute successful mass encirclements (Operation Bagration).

In 1945, things got so bad that the statistics system began to break down.

(In this sense, the German pattern was the inverse of the Soviet one, which had extremely high losses in 1941-42, which moderated in 1943, and either converged with or fell below German ones by 1944-45).

Regarding this question specifically, the answer is - not high. However, this would to a great extent depend on WHERE said soldier was serving. If he participated in the invasion of Poland and France, but was then shunted off to some out of the way garrison duty in a place like Crete, then his chances would be pretty good actually. However, they would decrease substantially if he was to see action in Italy and France, and decrease drastically if he was to be on the Eastern Front from Stalingrad on.

Can't speak about the likelihood, but there are a few prominent examples who made it though all the way. Nobel prize-winning writer Heinrich Böll (born 1917) fought the whole war (I only consulted his biography in German Wikipedia for this to check the dates, though), from September 1939 to April 1945. He was not even joining the Hitlerjugend as a kid growing up, so he wasn't favoured. Just lucky I guess (and we, his readers, are lucky for having him survived, as well). From english Wikipedia:

he served in France, Romania, Hungary and the Soviet Union, and was wounded four times (as well as contracting typhoid fever)

It would be interesting to know how many soldiers served on large numbers of fronts I.e. Blitz, Norway, North Africa, eastern front, Italy, back to the west.

That would also be true of British servicemen. Would it be possible to have served on more than 3 continents?