There’s a huge amount of space out there for them.
If you calculate the volume of space occupied by satellites from lowest orbit to highest, and divide by number of satellites, you find that each has, on average, millions of cubic kilometres all to itself.
The geostationary ones are all above the equator, and stay above points on the surface, so they will never cross paths.
On average, half of the orbital satellites, will be on one side of the Earth while the other half are on the other side further reducing the chance of crossed paths.
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