Woocommerce how to update variable product price programitically?

I believe you want the woocommerce_variable_price_html filter hook. But there are several price related filters listed in the official docs here:
WooCommerce Api Docs: Hooks

woocommerce_variable_price_html in 3.0 is defined in /class-wc-product-variable.php
https://docs.woocommerce.com/wc-apidocs/source-class-WC_Product_Variable.html#145

Hooking it with something like:

add_filter( 'woocommerce_variable_price_html', 'NAME_OF_YOUR_FUNCTION', 10, 2 );

Here is some Additional info on Filter Hooks in WordPress

There is also a woocommerce_variation_prices filter applied at line 221 of
class-wc-product-variable-data-store-cpt.php
https://docs.woocommerce.com/wc-apidocs/source-class-WC_Product_Variable_Data_Store_CPT.html#221