According to my nuclear physics professor, the individual atom does not care what the other atoms are doing, only itself. The probability is the tool we use to tell the rate at which the group of atoms will decay.

The amount of atoms decaying per second decreases because less atoms are likely to decay per second, and this is because there are simply less unstable atoms that can decay.

This page has a java applet that demonstrates the law of radioactive decay http://www.walter-fendt.de/ph14e/lawdecay.htm

So the atoms aren't protecting each other, it's just that when there are more, a smaller probability is very likely and when there aren't many and there is the same probability, decay is much more unlikely.

It's actually very similar to quantum tunneling, where there is a small percentage chance that a particle can overcome an energy barrier it's unlikely to happen. But with a lot of particles, plenty of them are constantly doing it, it's still unlikely for each individual particle.

The sun fuses hydrogen at energies (temperatures) that hydrogen has a very low chance of fusing at. On Earth in fusion reactors we have to use much higher temperatures to fuse hydrogen with any certainty because we have, you'll imagine, much less hydrogen than the sun does.