How to make a linearlayout filling remaining space in a relativelayout?

I've got a relativelayout with three linearlayouts as children. The last one has a fixed height and has android:layout_alignParentBottom set to "true". While the middle one is properly positioned below the first one, it goes as far as the bottom of the screen, so that its lower part is overlapped by the third one.

What's wrong?

Thanks

<?xml version="1.0" encoding="utf-8"?>
<RelativeLayout
    xmlns:android="http://schemas.android.com/apk/res/android"
    android:layout_width="fill_parent"
    android:layout_height="fill_parent" >

    <LinearLayout
        android:id="@+id/category"
        android:layout_width="fill_parent"
        android:layout_height="50dp"
        android:layout_alignParentTop="true"
        android:orientation="horizontal" >

        <ImageView
            android:id="@+id/back_btn"
            android:layout_width="29dp"
            android:layout_height="34dp"
            android:layout_gravity="center_vertical"
            android:src="@drawable/red_arrow_left" />

        <TextView
            android:id="@+id/cat_name"
            android:layout_width="fill_parent"
            android:layout_height="wrap_content"
            android:layout_gravity="center_vertical"
            android:gravity="center"
            android:textSize="20sp" />
    </LinearLayout>

    <LinearLayout
        android:layout_width="fill_parent"
        android:layout_height="fill_parent"
        android:layout_below="@+id/category"
        android:layout_marginTop="10dp"
        android:orientation="horizontal" >

        <ListView
            android:id="@+id/android:list"
            android:layout_width="fill_parent"
            android:layout_height="fill_parent"
            android:background="@android:color/white"
            android:cacheColorHint="@android:color/white" />

        <TextView
            android:id="@+id/android:empty"
            android:layout_width="fill_parent"
            android:layout_height="fill_parent"
            android:background="@android:color/white"
            android:cacheColorHint="@android:color/white"
            android:padding="10dp"
            android:text="@string/no_item" />
    </LinearLayout>

    <LinearLayout
        xmlns:android="http://schemas.android.com/apk/res/android"
        android:id="@+id/nav_bar"
        android:layout_width="fill_parent"
        android:layout_height="40dp"
        android:layout_alignParentBottom="true"
        android:orientation="horizontal" >
    //stuff

    </LinearLayout>
</RelativeLayout>