Customizing string format in a Caliburn.Micro convention bound TextBox

I have a WPF TextBox that is bound to a view-model number property Distance through Caliburn.Micro naming conventions. I want to be able to customize the TextBox string format while preserving the convention binding that Caliburn.Micro has set up. How should I do that?

From my View Model:

public double Distance
{
    get { return _distance; }
    set
    {
        _distance = value;
        NotifyOfPropertyChange(() => Distance);
    }
}

From my View:

<TextBox x:Name="Distance"/>

When the Distance is non-zero, I want to display the number with a fixed set of decimals, and when the Distance is zero I want the text box to be empty.

Using explicit binding I can bind the TextBox.Text property to Distance, and then I can set the StringFormat simultaneously:

<TextBox x:Name="Distance" Text="{Binding Distance, StringFormat=0.000;;#}"/>

However, the explicit Text binding would then short-circuit the Caliburn.Micro naming convention binding. Is it possible to customize the string format without simultaneously having to set the binding path of the TextBox.Text property, so that I can solely rely on Caliburn.Micro to handle the Distance-to-TextBox binding?