What is the probability of mining a block by a miner controlling a fraction of hashing power? Suppose a miner controls α fraction of the hashing power and the chain on which he is trying to mine has the mining rate given by f. How to find the probability of mining a block by the miner?
Probability
As  MCCCS comented:

Your hashrate divided by total hashrate is the probability of you finding the next block.

As of March 2021




Item
Hashrate MH/s




Typical desktop computer's i7 CPU
24


Antminer S19 Pro
110,000,000


Bitcoin network
156,000,000,000,000




So every ten minutes a CPU miner would have a 1 in 6,500,000,000,000 chance of earning 6.25 BTC. You have a 1 in 139,000,000 chance of winning the Euromillions lottery so lottery tickets will give you an overwhelmingly better return on investment in the longer term than does CPU mining. In both cases you are more likely to lose lots of money than see any profit.

&quot;Expected earnings&quot;
You can also key your hashrate into an online calculator to find your &quot;expected earnings&quot;.




Setting
Value
Units




Difficulty Factor
1.54660989356e+13



Hash Rate
24.0
MH/s


Exchange Rate
50809.85
($/BTC) [user]


BTC / Block
6.25000000





This Difficulty





Coins
Dollars




per Day
0.00000000 BTC
$0.00


per Week
0.00000000 BTC
$0.00


per Month
0.00000001 BTC
$0.00


this diff (est)
0.00000008 BTC
$0.00




Next Difficulty [estimated]





Coins
Dollars




per Day
0.00000000 BTC
$0.00


\per Week
0.00000000 BTC
$0.00


per Month
0.00000001 BTC
$0.00




Of course, you might get lucky.

References

https://www.blockchain.com/charts/hash-rate
https://alloscomp.com/bitcoin/calculator