The following XAML produces a run-time Binding error when I click on an item in the ListBox:

<Window
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:sys="clr-namespace:System;assembly=mscorlib"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    x:Class="WpfApplication1.MainWindow"
    x:Name="Window"
    Title="MainWindow"
    Width="640" Height="480">
    <Window.Resources>
        <x:Array x:Key="strings" Type="{x:Type sys:String}">
            <sys:String>one</sys:String>
            <sys:String>two</sys:String>
            <sys:String>three</sys:String>
            <sys:String>four</sys:String>
        </x:Array>
    </Window.Resources>
    <Grid>
        <ListBox
            DataContext="{StaticResource strings}"
            IsSynchronizedWithCurrentItem="True"
            ItemsSource="{Binding}"
            SelectedValuePath="{Binding /Length}">
            <ListBox.ItemTemplate>
                <DataTemplate>
                    <Grid>
                        <Grid.Resources>
                            <Style TargetType="{x:Type Label}">
                                <Setter Property="Background" Value="Yellow"/>
                                <Setter Property="Margin" Value="0,0,4,0"/>
                                <Setter Property="Padding" Value="0"/>
                            </Style>
                        </Grid.Resources>
                        <Grid.ColumnDefinitions>
                            <ColumnDefinition/>
                            <ColumnDefinition/>
                        </Grid.ColumnDefinitions>
                        <Grid.RowDefinitions>
                            <RowDefinition/>
                            <RowDefinition/>
                        </Grid.RowDefinitions>
                        <!-- Row 0 -->
                        <Label Grid.Column="0" Grid.Row="0">String:</Label>
                        <TextBlock
                            Grid.Column="1"
                            Grid.Row="0"
                            Text="{Binding}"/>
                        <!-- Row 1 -->
                        <Label Grid.Column="0" Grid.Row="1">Length:</Label>
                        <TextBlock
                            Grid.Column="1"
                            Grid.Row="1"
                            Text="{Binding Length, Mode=Default}"/>
                    </Grid>
                </DataTemplate>
            </ListBox.ItemTemplate>
        </ListBox>
    </Grid>
</Window>

This is the run-time Binding error message:

System.Windows.Data Error: 39 : BindingExpression path error: '3' property not found on 'object' ''String' (HashCode=1191344027)'. BindingExpression:Path=3; DataItem='String' (HashCode=1191344027); target element is 'ListBox' (Name=''); target property is 'NoTarget' (type 'Object')

I would like the selected value of the ListBox to be the Length of the selected String object. What is wrong with my SelectedValuePath Binding syntax? Are there any related issues with IsSynchronizedWithCurrentItem?