Kessler Syndrome is very unlikely in GEO orbits. The reason is twofold: first the distances are enormous, but more importantly all of the satellites are traveling at the same speed in the same direction. Even a defunct satellite that didn't get put in a parking orbit and starts drifting will take years before it even has a chance of colliding with another satellite, and the odds of that collision are infinitesimal.
In LEO you have a completely different story. The distances are still large, but not as overwhelming as they are in GEO. Also, satellites are flying in every direction at very high relative velocities to one another. A piece of space trash could have thousands of potential collisions per day, so even if the odds of any one collision are small the cumulative odds start to add up over time.
Of course the other problem is that when we put people into space we put them in LEO. People have not ventured beyond LEO since the Apollo program. In the event of a full blown Kessler syndrome manned space flight would have to be put on hold for decades while we wait for the skies to clear up.
In LEO you have a completely different story. The distances are still large, but not as overwhelming as they are in GEO. Also, satellites are flying in every direction at very high relative velocities to one another. A piece of space trash could have thousands of potential collisions per day, so even if the odds of any one collision are small the cumulative odds start to add up over time.
Of course the other problem is that when we put people into space we put them in LEO. People have not ventured beyond LEO since the Apollo program. In the event of a full blown Kessler syndrome manned space flight would have to be put on hold for decades while we wait for the skies to clear up.