user1307: I have problem finding this. The Bitcoin wiki mentions the probability here, but only with a link to the current value on BlockExplorer.
The wiki page on difficulty doesn't mention the formula for the probability either.

user208: If the current difficulty is D, then the target hash (the value below which block hashes must go) is:

0x00000000FFFF0000000000000000000000000000000000000000000000000000 / D

(by definition of difficulty, which is a fraction of the maximum target), or otherwise put, the number of valid hashes is:

65535 * 2208 / D

Which means that the ratio of all hashes over valid hashes would be:

2256 / (65535 * 2208 / D) =
  D * 248 / 65535 =
  D * 4295032833

Which, at the current (January 2017) difficulty of D =  392963262344.3704 means that one hash in

392963262344.3704 * 4295032833 = 1687790113931869416948

results in a valid block, or each attempt has a chance of

1 / 1687790113931869416948 = 0.000000000000000000059 %


1307: <p>I have problem finding this. The Bitcoin wiki mentions the probability <a href="https://en.bitcoin.it/wiki/Target#What_is_the_target_now.3F" rel="nofollow">here</a>, but only with a link to the <a href="http://blockexplorer.com/q/probability" rel="nofollow">current value on BlockExplorer</a>.</p>

<p>The wiki page on <a href="https://en.bitcoin.it/wiki/Difficulty" rel="nofollow">difficulty</a> doesn't mention the formula for the probability either.</p>
 208: <p>If the current difficulty is D, then the target hash (the value below which block hashes must go) is:</p>

<blockquote>
  <p>0x00000000FFFF0000000000000000000000000000000000000000000000000000 / D</p>
</blockquote>

<p>(by definition of difficulty, which is a fraction of the maximum target), or otherwise put, the number of valid hashes is:</p>

<blockquote>
  <p>65535 * 2<sup>208</sup> / D</p>
</blockquote>

<p>Which means that the ratio of all hashes over valid hashes would be:</p>

<blockquote>
  <p>2<sup>256</sup> / (65535 * 2<sup>208</sup> / D) =
  D * 2<sup>48</sup> / 65535 =
  D * 4295032833</p>
</blockquote>

<p>Which, at the current (January 2017) difficulty of D =  392963262344.3704 means that one hash in</p>

<blockquote>
  <p>392963262344.3704 * 4295032833 = 1687790113931869416948</p>
</blockquote>

<p>results in a valid block, or each attempt has a chance of</p>

<blockquote>
  <p>1 / 1687790113931869416948 = 0.000000000000000000059 %</p>
</blockquote>
