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I hadn't read about this before. From Wikipeida: The software of the probe runs on Nucleus RTOS operating system. Nucleus RTOS is a real-time operating system (RTOS) offered by the Embedded Software Division of Mentor Graphics for various central processing unit (CPU) platforms. Nucleus RTOS is embedded software and is in an estimated 2.11 billion devices worldwide. ... The Nucleus RTOS is designed for deeply embedded systems applications including consumer electronics, set-top boxes, cellular phones, and other portable and handheld devices. For limited memory systems Nucleus RTOS can be scaled down to a memory footprint as small as 13 KB for both code and data.

2.11 billion devices world wide, and 1 device beyond Pluto. The most wide spread operating system developed by the humans of Earth.

That means the average device running Nucleus RTOS is 3.5 kilometers from Earth.
And is rising at approximately 250 meters per year.
Have you accounted for the rise in quantity of terrestrial devices, or only used the increasing distance of New Horizons to calculate the 250 meters?
Good point, that didn't occur to me.
New Horizons is only about 33 AU from the sun. Voyager 1 is currently 133 AU from the sun, and is leaving faster than New Horizons; however I am not sure what os voyager is using.
Voyager spacecraft do not use any operating system. Due to the highly custom CPUs in Voyager, writing a compiler to build a 1970s era OS for the architecture would have been extremely risky and inefficient. It wasn't until the mid-1990s that the cultural restrictions on operating systems relaxed enough for some missions to start using them, and often times they are used for simple features like task scheduling and memory management because the vendors have already put the time into testing their implementations (which are well tested for other aerospace, telecom, medical, and automotive applications).

Until about 20 years ago, the complexity of the hardware didn't really necessitate off the shelf OSs anyway, and often times the overhead cost was too much to be practical anyway.

I was surprised to find that New Horizon is using Nucleus but I guess it makes sense since it was developed largely outside of the NASA-JPL west coast mafia (only slightly joking...). JPL has been using Wind River's VxWorks RTOS since the mid-1990s including on missions like Mars Pathfinder, the Mars Rovers, and most recently on the Mars Science Lab Curiosity. I don't have an authoritative list but if two missions running VxWorks are on opposite sides of the solar system (very likely) or on a slingshot out on the opposite side of Mars (less likely), VxWorks might take that most wide spread crown. It's definitely present on at least half a dozen active missions in the solar system.
Also - the open source RTEMS kernel is running on a few radios at Mars and elsewhere, including the Curiosity rover.