TL;DR: Depending on your definition of "alien probe", it was either Invaders From Mars (1953) or an episode of The Outer Limits called The Invisibles (1964).
It seems the first real-life claim of alien probing was made by a man named Barney Hill. Hill considered his story non-fiction, I know, but bear with me.
In January, 1964, Hill underwent a hypnosis session, and it was then that he first claimed that he and his wife Betty had been abducted by aliens. He first mentioned the probing thing at a later session, on February 22 of that year, and although the hypnosis session took place in 1964, it wasn't published until much later.
The Twilight Zone:
Here's where it gets interesting: In the February 22 hypnosis session, Hill said the aliens were wearing black jackets.
Here's a picture of the aliens from the Twilight Zone episode Black Leather Jackets:
When did this episode air, you ask? On January 31, 1964. Hill's aliens-in-black-leather-jackets story came less than a month later. Prior to January 31, Hill had mentioned aliens, but not leather jackets. Coincidence?
The Outer Limits:
On February 22, Hill also mentioned an anal probe for the first time. Here's a screen cap from an episode of The Outer Limits titled The Invisibles:
These images show agents of a shadowy organization called The Invisibles injecting someone with a crab-like alien parasite - basically, an alien probe.
When did this episode air, you ask? February 3, 1964. Hill's account of his own anal probe was made 19 days later. Coincidence?
It isn't strictly relevant here, but it is worth mentioning that a number of elements from Hill's February 22 account bear clear similarities to the February 10 and February 17 episodes of The Outer Limits as well.
Thus, the first real-life alien probe story was based on The Invisibles, which depicted one of the first alien probes in fiction.
Invaders From Mars:
I say "one of the first" because there might be one earlier example.
In the 1953 film Invaders From Mars, a woman is injected with a mind-control device through the back of the neck by a comically enormous machine with a needle attached.
Predictably, Hill claimed that his wife had suffered the attentions of a similar device, although in his story, the needle entered her navel. If you consider the scene from Invaders From Mars to be a probe, then this is probably the first example of an "alien probe" in fiction.
Basically, Hill liked his alien-based science fiction, and he composed his own story by copying elements of a movie, an episode of The Twilight Zone, and three episodes of The Outer Limits. All he did was take a needle in the neck and make it a needle in his wife's belly, and take an alien parasite on a guy back and make it an alien probe into his own butt. From such lowly origins, a comedy trope was born.