How to evaluate the probability of equihash?

I study the equihash algorithm about a few day.

But my math skill is poor and I have some question about how to measure difficulty and probability.

The current n,k is 200,9 means equihash need to use Equihash Generator create 2^21 amount hashs each has 200 bits length,

and I need to find 2^9 exactly same number from those 2^21 hashs.

My intuition is the probability of that is very very tiny,

But I don't know how magnitude it is.

and compare the birthday problem probability and the dynamic difficulty that zcash determine,

which probability is more little?

The only way I can use is the average block mining time is 150 seconds, and the zcash total solves is 170 million per second,

so about every 25 billion solves can mine a block,

means the dynamic difficulty probability * the birthday problem probability is 1 / 25B (Am I right?)

but how is the two probability weights are?

Thanks for your help.