The 1873 Closed 3 Three-Cent Nickel is a relatively common coin in Proof condition. The reported mintage of 1,100+ is based on the number of complete Proof sets sold in that year, plus an unknown number of "Minor" Proof sets (three-piece sets that contained only the Cent, Three-Cent Nickel, and Nickel). Considering that PCGS had certified 537 examples as of November 2011, the true mintage figure should probably be much higher, say in the 1,500-2,000 coin range.
The Closed 3 is the only Proof version of the 1873 Three-Cent Nickels. No "Open 3" Three-Cent Nickels are known to exist in Proof. On the Closed 3 version, the loops of the 3 were placed so close together that it is easy to mistake the 3 for an 8 at a casual glance. Treasury official noticed this early in 1873 and asked the Mint to correct the problem by "opening" the loops of the 3. This was done for virtually all coin types in 1873.
Though the 1873 Closed 3 Three-Cent Nickel is easy to locate in Proof condition, it is decidedly scarcer (by about half) than many of the dates in the 1880's (which have low circulation-strike mintages, but relatively high Proof mintages.
Cameo Proofs make up less than 20% of the existing population, at least according to the PCGS Population Report, but this percentage may be understated because PCGS has not always designated Proofs as Cameos or non-Cameos. On the other hand, Deep Cameos are either extremely rare or non-existent, as PCGS has certified none to date.
Superb Proofs are very rare. PCGS has graded 10 non-Cameo Proofs in PR-66 (and none finer), only a single PR67 Cameo, and, as already mentioned, no Deep Cameo Proofs.