Why Is the Probability of a Single Share Being a Valid Block Extremely Low?

The probability is extremely low because the network difficulty target for a valid block is orders of magnitude higher than the pool's share difficulty target. The network requires a hash that starts with a very long string of zeros, while a share only requires a shorter string of zeros.

A single share meeting the network difficulty is a rare event.

What Is the Relationship between Hash Rate and the Difficulty Target?
Why Is Volatility a More Dominant Factor than the Risk-Free Rate in Crypto Option Pricing?
How Does the Network’s Difficulty Target Relate to the Energy Expenditure in PoW?
If the Hash Rate Doubles, How Does the Difficulty Target Respond?
How Is the Difficulty of a pool’S’share’ Target Set Relative to the Network Difficulty?
In the Context of Options Trading, How Is the Relationship between Share Difficulty and Network Difficulty Analogous to “In-the-Money” Vs. “Out-of-the-Money”?
What Is a “Hash Rate” and How Does It Affect the Difficulty Target?
Does Unrealized Profit Count toward Meeting the Maintenance Margin?

Glossar