He didn’t get snagged because of an investigation into prostitution, his suspicious money transfers led to the investigation of the prostitutes:

The federal investigation of a New York prostitution ring was triggered by Gov. Eliot Spitzer’s suspicious money transfers, initially leading agents to believe Spitzer was hiding bribes, according to federal officials.
[…]
The suspicious financial activity was initially reported by a bank to the IRS which, under direction from the Justice Department, brought kin the FBI’s Public Corruption Squad.

“We had no interest at all in the prostitution ring until the thing with Spitzer led us to learn about it,” said one Justice Department official.
Spitzer, who made his name by bringing high-profile cases against many of New York’s financial giants, is likely to be prosecuted under a relatively obscure statute called “structuring,” according to a Justice Department official.
Structuring involves creating a series of financial movements designed to obscure the true purpose of the payments.