On the Windows Authenticated side of an extended web application with FBA, the people picker is only working when I also enable FBA through Central Administration for the Windows Authenticated web application.
When I enable FBA on the web application like so:

The people picker will pick up the FBA users without a problem. However, with both modes of authentication enabled, when you navigate to the Windows Authenticated site, you get a dropdown to choose your method of authentication rather than having the Windows credentials passed through:

Disabling FBA in the Edit Authentication modal allows the credentials to pass through, but you can not select FBA users in the people picker.
It's interesting to note that switching FBA on or off here has no effect on the web.config file.
Relevant web.config is set up as such:
<PeoplePickerWildcards>
<clear />
<add key="AspNetSqlMembershipProvider" value="%" />
<add key="FBAMembershipProvider" value="%" />
</PeoplePickerWildcards>
<membership defaultProvider="i">
<providers>
<add name="i" type="Microsoft.SharePoint.Administration.Claims.SPClaimsAuthMembershipProvider, Microsoft.SharePoint, Version=14.0.0.0, Culture=neutral, PublicKeyToken=71e9bce111e9429c" />
<add name="FBAMembershipProvider" type="System.Web.Security.SqlMembershipProvider, System.Web, Version=2.0.0.0, Culture=neutral, PublicKeyToken=b03f5f7f11d50a3a" applicationName="/" connectionStringName="FBADB" enablePasswordReset="true" enablePasswordRetrieval="false" passwordFormat="Hashed" requiresQuestionAndAnswer="false" requiresUniqueEmail="false" />
</providers>
</membership>
<roleManager cacheRolesInCookie="false" defaultProvider="c" enabled="true">
<providers>
<add name="c" type="Microsoft.SharePoint.Administration.Claims.SPClaimsAuthRoleProvider, Microsoft.SharePoint, Version=14.0.0.0, Culture=neutral, PublicKeyToken=71e9bce111e9429c" />
<add name="FBARoleProvider" type="System.Web.Security.SqlRoleProvider, System.Web, Version=2.0.0.0, Culture=neutral, PublicKeyToken=b03f5f7f11d50a3a" applicationName="/" connectionStringName="FBADB" />
</providers>
</roleManager>
<connectionStrings>
<add connectionString="Blah Blah Blah - This Works" name="FBADB" />
</connectionStrings>
The question is, how can I get the people picker to work without prompting the user to choose an authentication method at the time of login?