Windows – Huh? JDK not found? (on Windows 7 64-bit)

I am setting up a development environment for the latest Android 2.3 on a fresh install of Windows 7 64-bit.

I first installed the 64-bit JDK 6 (jdk-6u23-windows-x64.exe).
Then, I installed 64-bit Eclipse Classic 3.6 (eclipse-SDK-3.6.1-win32-x86_64.zip).
Then, I proceed to install the Android SDK Starter Package: installer_r08-windows.exe.

But… upon start it says: "Java SE Development Kit (JDK) not found."

Why? I just installed it.

Is this a mismatch between 32-bit and 64-bit?

How do I solve this?

Update (1): I tried setting the %JAVA_HOME% environment variable, as well as setting the Installed JREs in Eclipse, as suggested below. None of these solved the problem.

It appears that I am not the only experiencing the problem, as this thread suggests:
https://stackoverflow.com/questions/1919340/android-sdk-setup-under-windows-7-pro-64-bit

I wonder whether there is a 64-bit version of the Android SDK.

Update (2): I used the zip version instead (android-sdk_r08-windows.zip), ran android.bat, updated all SDK packages, and installed the ADT plugin (8.0.1), not before having to check: 'Contact all update sites during install to find required software'.

We'll see how this goes…

Update (3): It worked! (going to accept @bubu's answer shortly) — but why doesn't the emulator include the HelloAndroid app when I run it (Ctrl+F11) from Eclipse?